Fencing the Electronic Frontier (I)

Something’s come onto the digital frontier radar screen – it’s big, slow, flying low, and riddled with OCR errors. Look up Senate Bill 2796, and read it with me. I got mine from the Senate Legislative Information system, which led me here, and finally to the PDF file, the text from which I’ve pasted below.

Why should you care about this? Because it tells us that the Philippine government is definitely, steadily moving onto the digital frontier, and it seems like the Senate committees are, at least, beginning to understand that the Internet isn’t just a “collection of tubes”:

  • This provides children additional indirect protection under the law – it specifically identifies creation and distribution of child pornography as a punishable offense.
  • If you’ve been more than marginally irritated by unsolicited, commercial electronic spam, SB 2796 has something for you.
  • If you use Facebook (defined in this law as a service provider, apparently), this law affects your rights in the Philippine jurisdiction.
  • If you use a computer regularly in your electronic communications – this includes your touch phone, your work and home computer, your iDevice – this law has something for you as well.

Interested yet? I’ve a few more things to say about this; but for now, here’s the full text of Senate Bill 2796

SB. No. 2796

Prepared jointly by the Committees on Science and Technology; Constitutional Amendments, Revision of Codes and Laws; Education; Arts and Culture; Justice and Human Rights; Trade and Commerce; Public Information and Mass Media and Finance with Senators’ Trillanes, Angara, Enrile, Estrada, Lapid, Villar, Defensor Santiago, Marcos and Revilla as authors.


Be it enacted by the Senate and the House of Representatives of the Philippines in Congress assembled:


SECTION 1. Title. — This Act shall be known as the “Cybercrime Prevention
Act of 2011”,

SEC. 2. Declaration of Policy. — The State recognizes the vital role of information and communications industries such as content production, telecommunications, broadcasting, electronic commerce, and data processing, in the nation’s overall social and economic development. The State also recognizes the importance of providing an environment conducive to the development, acceleration, and rational application and exploitation of information and communications technology to attain free, easy, and intelligible access to exchange and/or delivery of information; and the need to protect and safeguard the integrity of computer, computer and communications systems, networks, and databases, and the confidentiality, integrity, and availability of information and data stored therein, from all forms of misuse, abuse, and illegal access by making punishable under the law such conduct or conducts. In this light, the State shall adopt sufficient powers to effectively prevent and combat such offenses by facilitating their detection, investigation, and prosecution at both the domestic and international levels, and by providing arrangements for fast and reliable international cooperation,

SEC. 3. Definition of Terms. — For purposes of this Act, the following terms
are hereby defined as follows:

a) Access – refers to the instruction, communication with, storing data in, retrieving data from, or otherwise making use of any resources of a computer system or communication network;

b) Alteration – refers to the modification or change, in form or substance, of an existing computer data or program;

c) Communication – refers to the transmission of information inclnding voice and non-voice data;

d) Computer system – means any device or a group of interconnected or related devices, one or more of which, pursuant to a program, performs automatic processing of data. It covers any type of computer device including devices with data processing capabilities like mobile phones and also computer networks. The device consisting of hardware and software may include input, output and storage facilities which may stand alone or be connected in a network or other similar devices. It also includes computer-data storage devices or medium.

e) Computer Data – refers to any representation of facts, information, or concepts in a form suitable for processing in a compnter system including a program suitable to cause a computer system to perform a function and includes electronic documents and/or electronic data messages;

f) Computer Program – refers to a set of instructions executed by the computer;

g) Without Right – refers to either: (l) conduct undertaken without or in excess of authority; or (ii) conduct not covered by established legal defenses, excuses, court orders, justifications, or relevant principles under the law;

h) Database – refers to a representation of information, knowledge, facts, concepts, or instructions which are being prepared, processed or stored or have been prepared, processed or stored in a formalized manner and which are intended for use in a computer system;

i) Interception – refers to listening to, recording, monitoring or surveillance of the content of communications, including procuring of the content of data, either directly, through access and use of a computer system or indirectly, through the use of electronic eavesdropping or tapping devices, at the same time that the communication is occurring;

j) Service Provider – refers to :

i. any public or private entity that provides to users of its service the ability to communicate by means of a computer system, and

ll. any other entity that processes or stores computer data on behalf of such communication service or users of such service;

k) Subscriber’s Information – refers to any information contained in the form of computer data or any other form that is held by a service provider, relating to subscribers of its services other than traffic or content data and by which can be established;
i. The type of communication service used, the technical provisions
taken thereto and the period of service;
ll. The subscriber’s identity, postal or geographic address, telephone and
other access numbers, any assigned network address, billing and
payment information, available on the basis of the service agreement
or arrangement;
iii. Any other available information on the site of the installation of
communication equipment, available on the basis of the service
agreement or arrangement.

I) Traffic Data or Non-Content Data – refers to any computer data other than the content of the communication, including but not limited to the communication’s origin, destination, route, time, date, size, duration, or type of underlying service.



SEC. 4. Cybercrime Offenses. — The following acts constitute the offense of cybercrime punishable under this Act:

A. Offenses against the confidentiality, integrity and availability of computer data and systems:

1. Illegal Access – The intentional access to the whole or any part of a computer system without right.

. Illegal Interception – The intentional interception made by technical means without right of any non-public transmission of computer data to, from, or within a computer system including electromagnetic emissions from a computer system carrying such computer data: Provided, however, That it shall not be unlawful for an officer, employee, or agent of a service provider, whose facilities are used in the transmission of communications, to intercept, disclose, or use that communication in the normal course of his employment while engaged in any activity that is necessary to the rendition of his service or to the protection of the rights or property of the service provider, except that the latter shall not utilize service observing or random monitoring except for mechanical or service control quality checks;

. Data interference – the intentional or reckless alteration of computer data without right.

. System Interference – the intentional or reckless hindering without right of the functioning of a computer system by inputting, transmitting, deleting or altering computer data or program.

. Misuse of Devices –

a. The use, production, sale, procurement, importation, distribution, or otherwise making available, without right, of:

. a device, including a computer program, designed or adapted primarily for the purpose of committing any of the offenses under this Act; or
. a computer password, access code, or similar data by which the whole or any part of a computer system is capable of being accessed with intent that it be used for the purpose of committing any of the offenses under this Act;.

b. The possession of an item referred to in paragraphs 5(a)(i) or (ii) above with intent to use said devices for the purpose of committing any of the offenses under this Section. Provided, That no criminal liability shall attach when the use, production, sale, procurement, importation, distribution, or otherwise making available, or possession of computer devices/data referred to is for the authorized testing of a computer system.

B. Computer-related Offenses:

1. Computer-related Forgery – (a) the intentional input, alteration, or deletion of any computer data without right resulting in inauthentic data with the intent that it be considered or acted upon for legal purposes as if it were authentic, regardless whether or not the data is directly readable and intelligible; (b) the act of knowingly using computer data which is the product of computer-related forgery as defined herein, for the purpose of perpetuating a fraudulent or dishonest design.

. Computer-related Fraud – the intentional and unauthorized input, alteration, or deletion of computer data or program or interference in the functioning of a computer system, causing damage thereby, with the intent of procuring an economic benefit for oneself or for another person or for the perpetuation of a fraudulent or dishonest activity; Provided, that if no damage has yet been caused, the penalty imposable shall be one degree lower.

C. Content-related Offenses:

1. Cybersex – any person who establishes, maintains or controls, directly or indirectly, any operation for sexual activity or arousal with the aid of or through the use of a computer system, for a favor or consideration.

2. Child Pornography – refers to any representation, whether visual, audio, or written combination thereof, by electronic, mechanical, digital, optical, magnetic or any other means, of child engaged or involved in real or simulated explicit sexual activities.

For the purpose of this Act, a “child” refers to a person below eighteen (18) years of age or over, but is unable to fully take care of himself/herself from abuse, neglect, cruelty, exploitation or discrimination because of a physical or mental disability or condition. A child shall also refer to: (a) a person regardless of age who is presented, depicted or portrayed as a child as defined herein; and (b) computer-generated, digitally or manually crafted images or graphics of a person who is represented or who is made to appear to be a child as defined herein.

The unlawful or prohibited acts constituting child pornography shall be defined and punishable by Republic Act No. 9775 or the Anti-Child Pornography Law.

3. Unsolicited Commercial Communications. — The transmission of commercial electronic communication with the use of computer system which seek to advertise, sell, or offer for sale products and services are prohibited unless:

a. There is a prior affirmative consent from the recipient; or
b. The following conditions are present:
i. The commercial electronic communication contains a simple, valid, and reliable way for the recipient to reject receipt of further commercial electronic messages (‘opt-out’) from the same source;
ii. The commercial electronic communication does not purposely disguise the source of the electronic message; and
iii. The commercial electronic communication does not purposely include misleading information in any part of the message in order to induce the recipients to read the message.

SEC. 5. Other Offenses. — The following acts shall also constitute an offense:
. Aiding or Abetting in the Commission of Cybercrime. — Any person who willfully abets or aids in the commission of any of the offenses enumerated in this Act shall be held liable.

. Attempt in the Commission of Cybercrime – Any person who willfully attempts to commit any of offenses enumerated in this Act shall be held liable.

SEC. 6. Liability under Other Laws. — A prosecution under this Act shall be without prejudice to any liability for violation of any provision of the Revised Penal Code, as amended or special laws.


SEC. 7. Penalties. — Any person found guilty of any of the punishable acts ennmerated in Sections 4A and 4B of this Act shall be punished with imprisonment of prision mayor or a fine of at least Two Hundred Thousand Pesos (PhP200,000.00) up to a maximum amount commensurate to the dan1age incurred or both.

Any person found guilty of any of the punishable acts enumerated in Section 4C(1) of this Act shall be punished with imprisonment of prision mayor or a fine of at least Two Hundred Thousand Pesos (PhP200,000.00) but not exceeding One Million Pesos (PhPl ,000,000.00) or both.

Any person found guilty of any of the punishable acts enumerated in Section 4C(2) of this Act shall be punished with the penalties as enumerated in Republic Act 9775 or the Anti-Child Pornography Act of 2009.

Any person found guilty of any of the punishable acts enumerated in Section 4C(3) shall be punished with imprisonment of arresto mayor or a fine of at least Fifty Thousand Pesos (PhP50,000.00) but not exceeding Two Hundred Fifty Thousand Pesos (PhP250,000.00) or both.

Any person found guilty of any of the punishable acts enumerated in Section 5 shall be punished with imprisonment one degree lower than that of the prescribed penalty for the offense or a fine of at least One Hundred Thousand Pesos (PhPIOO,OOO.OO) but not exceeding Five Hundred Thousand Pesos (PhP500,000.00) or both.

SEC. 8. Corporate Liability. — When any of the punishable acts herein defined are knowingly committed on behalf of or for the benefit of a juridical person, by a natural person acting either individually or as part of an organ of the juridical person, who has a leading position within in, based on (a) a power of representation of the juridical person, (b) an authority to take decisions on behalf of the juridical person, or (c) an authority to exercise control within the juridical person, the juridical person shall be held liable for a fine equivalent to at least double the fines imposable in Section 7 up to a maximum of Ten Million Pesos (PhplO,OOO,OOO.OO).

If the commission of any of the punishable acts herein defined was made possible due to the lack of supervision or control by a natural person referred to and described in the preceding paragraph, for the benefit of that juridical person by a natural person acting under its authority, the juridical person shall be held liable for a fine equivalent to at least double the fines imposable in Section 7 up to a maximum of Five Million Pesos (Php5,000,000.00).

The liability imposed on the juridical person shall be without prejudice to the criminal liability of the natural person who has committed the offence.


SEC. 9. Real-time Collection of Computer Data. — Law enforcement authorities, with due cause, and upon securing a court warrant, shall be authorized to collect or record by technical or electronic means, and service providers are required to collect or record by technical or electronic means, and/or to cooperate and assist law enforcement authorities in the collection or recording of, traffic data, in real-time, associated with specified communications transmitted by means of a computer system.

SEC. 10. Preservation Of Computer Data. — The integrity of traffic data and subscriber information relating to communication services provided by a service provider shall be preserved for a minimum period of six (6) months from the date of the transaction. Content data shall be similarly preserved for six (6) months from the data of receipt of the order from law enforcement authorities requiring its preservation.

Law enforcement authorities may order a one-time extension for another six (6) months provided that once computer data preserved, transmitted or stored by a service provider is used as evidence in a case, the mere furnishing to such service provider of the transmittal document to the Office of the Prosecutor shall be deemed a notification to preserve the computer data until the termination of the case.

The service provider ordered to preserve computer data shall keep confidential the order and its compliance.

SEC. 11. Disclosure of Computer Data. — Law enforcement authorities, upon securing a court warrant, shall issue an order requiring any person or service provider to disclose or submit subscriber’s information, traffic data or relevant data in his/its possession or control within seventy two (72) hours from receipt of the order in relation to a valid complaint officially docketed and assigned for investigation and the disclosure is necessary and relevant for the purpose of investigation.

SEC. 12. Search, Seizure, and Examination of Computer Data. — Where a search and seizure warrant is properly issued, the law enforcement authorities shall likewise have the following powers and duties:

Within the time period specified in the warrant, to conduct interception, as defined in this Act, content of communications, procure the content of data either directly, through access and use of computer system, or indirectly, through the use of electronic eavesdropping or tapping devices, in real time or at the same time that the communication is occurring and:

a. To secure a computer system or a computer data storage medium;
b. To make and retain a copy of those computer data secured;
c. To maintain the integrity of the relevant stored computer data;
d. To conduct examination of the computer data storage medium; and
e. To render inaccessible or remove those computer data in the accessed computer or computer and communications network.

Pursuant thereof, the law enforcement authorities may order any person who has knowledge about the functioning of the computer system and the measures to protect and preserve the computer data therein to provide, as is reasonable, the necessary information, to enable the undertaking of the search, seizure and examination.

Law enforcement authorities may request for an extension of time to complete the examination of the computer data storage medium and to make a return thereon but in no case for a period longer than thirty (30) days from date of approval by the court.

SEC. 13. NOll-compliance. — Failure to comply with the provisions of Chapter IV hereof specifically the orders from law enforcement authorities shall be punished as a violation of P.D. No. 1829 with imprisonment of prision correctional in its maximum period or a fine of One Hundred Thousand Pesos (PhplOO,OOO.OO) or both, for each and every non-compliance with an order issued by law enforcement authorities.

SEC. 14. Duties of Law Enforcement Authorities. — To ensure that the technical nature of cybercrime and its prevention is given focus and considering the procedures involved for international cooperation, law enforcement authorities specifically the computer or technology crime divisions or units responsible for the investigation of cybercrimes are required to submit timely and regular repOlis including pre-operation, post-operation and investigation results and such other documents as may be required to the Department of Justice (DOJ) for review and monitoring.

SEC. I5. Jurisdiction. — The Regional Trial Court shall have jurisdiction over any violation of the provisions of this Act including any violation committed by a Filipino national regardless of the place of commission. Jurisdiction shall lie if any of the elements was committed within the Philippines or committed with the use of any computer system wholly or partly situated in the country, or when by such commission any damage is caused to a natural or juridical person who, at the time the offense was committed, was in the Philippines.

SEC. 16. General principles relating to international cooperation. — All relevant international instruments on international cooperation in criminal matters, arrangements agreed on the basis of uniform or reciprocal legislation, and domestic laws, to the widest extent possible for the purposes of investigations or proceedings concerning criminal offenses related to computer systems and data, or for the collection of evidence in electronic form of a criminal offense shall be given full force and effect.

SEC. 17. Applicability of the Convention on Cybercrime. — The provisions of Chapter III of the Convention on Cybercrimc shall be directly applicable in the implementation of this Act as it relates to international cooperation taking into account the procedural laws obtaining in the jurisdiction.

SEC. 18. Department of Justice. – The Department of Justice (DOJ) shall be responsible for extending immediate assistance for the purpose of investigations or proceedings concerning criminal offenses related to computer systems and data, or for the collection of electronic evidence of a criminal offense and to otherwise ensure that the provisions of this law are complied. In this regard, there is hereby created a DOJ Office of Cybercrime for facilitating or directly carrying out the provisions of technical advice, preservation of data, collection of evidence, giving legal information and locating suspects and all other cybercrime matters related to investigation and reporting issues.

SEC. 19. Commission on Information and Communications Technology. – The Commission on Information and Communications Technology (CICT) shall be responsible for formulating and implementing a national cyber security plan and extending immediate assistance for the suppression of real-time commission of cybercrime offenses through a computer emergency response team (CERT). In this regard, there is hereby created a CICT National Cyber Security Office to carry out the above responsibilities and all other matters related to cybercrime prevention and suppression, including capacity building.


SEC 20. Cybercrime Investigation and Coordinating Cellter, — There is hereby created, within thirty (30) days from the effectivity of this Act, a Cybercrime Investigation and Coordinating Center, hereinafter referred to as CICC, under the control and supervision of the Office of the President, to formulate and implement the national cyber security plan.

SEC 21. Composition. — The CICC shall be headed by the Chairman of the Commission on Information and Communications Technology as Chairman; with the Director of the NBI as Vice-Chairman; Chief of the PNP; Chicf of the National Prosecution Service (NPS); and the Head of the National Computer Center (NCC) as members.

The CICC shall be manned by a secretariat of selected personnel and representatives from the different participating agencies.

SEC. 22. Powers and Functions. — The CICC shall have the following powers and functions:
a. To prepare and implement appropriate and effective measures to prevent and suppress cybercrime activities as provided in this Act;
b. To monitor cybercrime cases being handled by participating law enforcement and prosecution agencies;
c. To facilitate international cooperation on intelligence, investigations, training and capacity building related to cybercrime prevention, suppression and prosecution;
d. To coordinate the support and participation of the business sector, local government units, and non-government organizations in cybercrime prevention programs and other related projects;
e. To recommend the enactment of appropriate laws, issuances, measures and policies;
f. To call upon any government agency to render assistance m the accomplishment of the Clee’s mandated tasks and functions;
g. To perform such other functions and duties necessary for the proper implementation of this Act.


SEC 23. Appropriations. — The amount of ten million pesos (PhplO,OOO,OOO.OO) shall be appropriated annually for the implementation of this Act.

SEC 24. Implementing Rules and Regulations. – The Department of Justice in consultation with the Commission on Information and Communication Technology shall formulate the necessary rules and regulations for the effective implementation ofthis Act including the creation and establishment of a national cyber security office with the relevant computer emergency response councilor team.

SEC 25. Separability Clause. — If any provision of this Act is held invalid, the other provisions not affected shall remain in full force and effect.

SEC 26. Repealing Clause. –. All laws, decrees, or rules inconsistent with this Act are hereby repealed or modified accordingly. Section 33 of Republic Act No. 8792 or the Electronic Commerce Act is hereby modified accordingly.


See the article on Interaksyon.com.

Calculus Outline – Louis M. Leithold 6/e

  1. FUNCTIONS OF A SINGLE REAL VARIABLE – Limits and continuity – Complete discussion includes proofs of all theorems in the body of the chapter as well as in the exercises. Horizonal asymptotes, limits at infinity, vertical asymptotes and infinite limits are discussed.
    1. The limit of a function (56)
    2. Theorems on limits of functions (64)
    3. One side limits (73)
    4. Infinite limits (78)
    5. Limits at infinity (88)
    6. Continuity of a function at a number (98)
    7. Continuity of a composite function and continuity on an interval (107)
    8. Continuity of the trigonometric functions and the squeeze theorem (114)
    9. Proofs of some theorems on limits of functions (Supplementary) (122)
    10. Additional theorems on limits of functions (131)

    Continue reading “Calculus Outline – Louis M. Leithold 6/e”

An outline of calculus topics

Found my outline! It’s the table of contents for the textbook The Calculus with Analytic Geometry, 6th Edition, by Louis M. Leithold. This was the text from which I learned everything of undergraduate calculus, from limits to Green’s functions and basis vectors and multiple integrals, well over a decade ago. My first copy had eventually become all dogeared and coffee-stained from hours of poring through the text over three semesters of coursework; the second copy fared no better, as it saw me through the last of three semesters, and one more taking in differential equations.  I’d typed in the table of contents to serve as my weekly reading guide; those were busy days.

What’s particularly good about TCWAG is that it provides clear step-by-step proofs of all theorems and major results, unlike free texts offered up by MIT through it’s Open Courseware program (see Calculus, by Gilbert Strang, at http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/). Only rarely did we encounter use of results that could not be developed as part of an introductory calculus course – these were clearly identified as, for example, in the case of the completeness axiom, which could only be fully developed in a course in real analysis.

In all there are 18 chapters, which we’d covered at a rate of about six chapters per semester. This outline will serve as my guide to retrieving the calculus in the next few months.

  1. FUNCTIONS OF A SINGLE REAL VARIABLE– Limits and continuity – Complete discussion includes proofs of all theorems in the body of the chapter as well as in the exercises. Horizonal asymptotes, limits at infinity, vertical asymptotes and infinite limits are discussed.
    1. The limit of a function (56)
    2. Theorems on limits of functions (64)
    3. One side limits (73)
    4. Infinite limits (78)
    5. Limits at infinity (88)
    6. Continuity of a function at a number (98)
    7. Continuity of a composite function and continuity on an interval (107)
    8. Continuity of the trigonometric functions and the squeeze theorem (114)
    9. Proofs of some theorems on limits of functions (Supplementary) (122)
    10. Additional theorems on limits of functions (131)
  2. The derivative and differentiation– The classical geometrical interpretation of the derivative, detailed derivative evaluation, concise proofs of theorems on differentiation, derivatives of trig functions, and the Chain Rule.
    1. The tangent line and the derivative (139)
    2. Differentiability and continuity (148)
    3. Theorems on differentiation of algebraic functions (156)
    4. Rectilinear motion and the derivative as a rate of change (163)
    5. Derivatives of the trigonometric functions (173)
    6. The derivative of a composite function and the Chain Rule (181)
    7. The derivative of the power function for rational exponents (190)
    8. Implicit differentiation (195)
    9. Related rates (199)
    10. Derivatives of higher order (205)
  3. Function extremaTechniques of graphing The differential – Theorems on extrema and graph behavior motivate a complete method for function graph sketching. Differentials are treated in this section, adjacent to differentiation subject matter.
    1. Maximum and minimum function values (217)
    2. Applications involving an absolute extremum on a closed interval (224)
    3. Rolle’s theorem and the Mean-value theorem (230)
    4. Increasing and decreasing functions and the first-derivative test (236)
    5. Concavity and points of inflection (241)
    6. The second-derivative test for relative extrema (249)
    7. Drawing the sketch of the graph of a function (254)
    8. Further treatment of absolute extrema and applications (260)
    9. The differential (269)
    10. Numerical solutions Newton’s method (277)
  4. The definite integralIntegration – Indefinite integration, area, the definite integral, the Fundamental Theorem of the Calculus. Trapezoidal and parabolic rules, formulas for error bound estimation.
    1. Antidifferentiation (286)
    2. Some techniques of antidifferentiation (295)
    3. Differential equations and rectilinear motion (303)
    4. Area (312)
    5. The definite integral (324)
    6. Properties of the definite integral (331)
    7. The mean-value theorem for integrals (340)
    8. The fundamental theorems of the calculus (344)
    9. Area of a plane region (352)
    10. Numerical integration (supplementary) (359)
  5. Applications of the definite integral– Evaluation techniques and principles are discussed, supported by concise motivation and explanations. Applications in physics.
    1. Volumes by slicing, disks, and washers (374)
    2. Cylindrical-shell method (383)
    3. Length of arc of the graph of a function (388)
    4. Center of mass of a rod (394)
    5. Centroid of a plane region (400)
    6. Work (407)
    7. Liquid pressure (supplementary) (413)
  6. Inverse, logarithmic and exponential functions– Includes a concise definition of irrational numbers. Applications.
    1. Inverse functions (422)
    2. Inverse function theorems Derivative of a function inverse (431)
    3. The natural logarithmic function (439)
    4. Logarithmic differentiation Integrals yielding ln(x) (449)
    5. The natural exponential function (455)
    6. Other exponential and logarithmic functions (463)
    7. Applications (469)
    8. First-order linear differential equations (supplementary) (481)
    9. Review (492)
  7. Inverse trigonometric and hyperbolic functions.
    1. The inverse trigonometric functions (496)
    2. Derivatives of the inverse trigonometric functions (503)
    3. Integrals yielding inverse trigonometric functions (510)
    4. Hyperbolic functions (514)
    5. Inverse hyperbolic functions (supplementary) (523)
    6. Review (527)
  8. Techniques of integration– Computational methods encountered in practical problems. Crucial examples illustrate the principles involved.
    1. Integration by parts (531)
    2. Of powers of sine and cosine (537)
    3. Of powers of tangent, cotangent, secant and cosecant (542)
    4. By trigonometric substitution (545)
    5. By partial fractions: linear (551)
    6. By partial fractions: quadratic denom. fact (561)
    7. Miscellaneous substitutions (566)
    8. Integrals yielding inverse hyperbolic functions (supplementary) (570)
    9. Review (575)
  9. The conic sections and polar coordinates.
    1. The parabola and translation of axes (578)
    2. The ellipse (586)
    3. The hyperbola (594)
    4. Rotation of axes (604)
    5. Polar coordinates (608)
    6. Graphs of equations in polar coordinates (614)
    7. Area of a region in polar coordinates (625)
    8. A unified treatment of conic sections and polar equations of conics (629)
    9. Tangent lines of polar curves (supplementary) (638)
    10. Review (647)
  10. Indeterminate forms, improper integrals, and Taylor’s formula– Concepts supporting a discussion on infinite series are assayed. Probability density function.
    1. The indeterminate form 0/0 (651)
    2. Other indeterminate forms (660)
    3. Improper integrals with infinite limits of integration (665)
    4. Other improper integrals (673)
    5. Taylor’s formula (677)
    6. Review (684)
  11. INFINITE SERIES– Sequences and infinite series – Theorems. Tests for convergence of a series.
    1. Sequences (687)
    2. Monotonic and bounded sequences (694)
    3. Infinite series of constant terms (700)
    4. Infinite series: Four theorems (709)
    5. Infinite series of positive terms (713)
    6. The integral test (723)
    7. Alternating series (726)
    8. Absolute and conditional convergence Ratio test Root test (731)
    9. Summary of convergence tests for infinite series (738)
    10. Review (740)
  12. Power series.
    1. Introduction to power series (743)
    2. Differentiation of power series (750)
    3. Integration of power series (760)
    4. Taylor series (767)
    5. The binomial series (776)
    6. Review (780)
  13. VECTOR-VALUED AND MULTIVARIABLE FUNCTIONS– Vectors in the plane and parametric equations.
    1. Vectors in the plane (783)
    2. Dot product (794)
    3. Vector-valued functions Parametric equations (801)
    4. Calculus of vector-valued functions (808)
    5. Length of arc (814)
    6. The unit tangent and normal vectors Arc length as parameter (820)
    7. Curvature (824)
    8. Plane motion (832)
    9. Tangential and normal components of acceleration (838)
    10. Review (842)
  14. 3D Vectors and solid analytic geometry.
    1. R^3 space (846)
    2. Vectors in R^3 (852)
    3. Planes (861)
    4. Lines in R^3 (868)
    5. Cross product (873)
    6. Cylinders and surfaces of revolution (883)
    7. Quadric surfaces (888)
    8. Curves in R^3 (894)
    9. Cylindrical and spherical coordinates (901)
    10. Review (905)
  15. INTRODUCTION TO MULTIVARIATE CALCULUS– Differential calculus of functions of more than one variable – Extensions of 1V calculus.
    1. Functions of more than one variable (908)
    2. Limits (917)
    3. Continuity (927)
    4. Partial derivatives (931)
    5. Differentiability Total differentials (939)
    6. The Chain Rule (949)
    7. Higher-order partial derivatives (956)
    8. Sufficient conditions for differentiability (963)
    9. Review (968)
  16. Directional derivatives, gradients, and applications of partial derivatives– Vector fields. Solution of extrema problems and Lagrange multipliers. Exact differential equation solution.
    1. Directional derivatives and gradients (972)
    2. Tangent planes and normals to surfaces (979)
    3. Extrema of functions of two variables (983)
    4. Lagrange multipliers (997)
    5. Obtaining a function from its gradient and exact differentials (1003)
    6. Review (1011)
  17. Multiple integration
    1. The double integral (1014)
    2. Double and iterated integrals (1019)
    3. Center of mass and moments of inertia (1026)
    4. The double integral in polar coordinates (1031)
    5. Area of a surface (1036)
    6. Triple integrals (1041)
    7. Triple integrals in cylindrical and spherical coordinates (1046)
    8. Review (1052)
  18. Introduction to the calculus of vector fields– Intuitive appproach to problems in physics and engineering.
    1. Vector fields (1056)
    2. Line integrals (1064)
    3. Line integrals independent of path (1072)
    4. Green’s theorem (1082)
    5. Surface integrals (1095)
    6. Gauss’s Divergence Theorem and Stokes’s Theorem (1102)
    7. Review (1108)

I’ll head off to a local bookstore in about thirty minutes to see whether this text is even still in distribution – I’m sure that I’ll at least be able to order a copy from overseas.


Can’t sleep: My mind is wandering about in my skull, a kitty among the bins. I can’t make up my mind how to represent an atomic algebraic expression term.

Clearly, an expression term, and an elementary binary operator are two different kinds of objects. What do I make, then, of an expression term such as sin(x)? It’s a function operator taking a single argument. I’d like to be able to manipulate a pair of rational expressions like


How about 2x? It’s an elementary product expression consisting of a constant and a variable. I’m beginning to think each subexpression ought to be represented as an object, now – so that I could replace the factor 2 with an expression, for example. This pretty much puts paid to representing an algebraic polynomial term as a struct:

struct Monomial {
    integer coeff;
    Variable x;
    Exponent t;

Each member coeff, x,  and t would then be an Expr:

struct Monomial {
    Expr coeff;
    Expr x;
    Expr t;

Then I should represent elementary operations as functors as well, perhaps. Hmm. This eliminates the need for a Monomial type:

Expr x('x'), X;
X = 2 * x ^ 3;
cout << X.strict().toString() << endl; // 2*(x^3)
cout << X.toHumanString() << endl; // 2x3
cout << X.toMathML() << endl; // Something like 2x(super)3

I need to look into operator associativity rules and find out whether any combination of member and nonmember functions will cause type coercion of the RHS into an Expr type.


My goal is to be able to create simple code to generate elementary algebra expressions programmatically, like so:

Expr a('a', '1/(x+2)');
Expr b('b', '2/(x+7)');
Expr c;
c = a * b;
cout << c.toMathML() << endl;
cout << c.execute().toMathML() << endl; // 1/(x^2 + 9x + 14)

Then a simple, short chunk of code could do and generate an online algebra workbook of arbitrary complexity:

string generate_rational_fraction_sum( int terms, int glbpower, int lubpower ) {
  Expr rfs;
  Expr numerator;
  Expr denominator;
  Expr monomial('x');
  for ( int i = 0 ; i < terms ; i++ ) {
    integer r = rand(glbpower, lubpower);
    integer q = rand(1,10);
    for ( int j = 0 ; j < r ; j++ ) {
      // Generate an order-j polynomial expression for the denominator
      integer k = rand(1,10);
      denominator += k * monomial ^ j;
    numerator = rand(1,10);
    rfs += numerator / denominator;
  return rfs.execute().toMathML();

Recovering Lost Sectors

Trigonometric identities – gone.  Techniques for polynomial factoring – gone. Ditto for logarithmic and exponential functions. Drat!

I guess recovering the calculus is basically going to take a wholesale rebootstrap of my entire maths education. Granted, a lot of it is going to be recovery rather than reintroduction. The skills have atrophied, and the surety of technique gone, but the memory of how to construct a proof, for example – the concept of inductive logic – isn’t completely lost to me.

This feels like having fallen off a mountain, nevertheless.

“Anybody have pitons?” I got pitons. The idea I have is to do both relearn algebra and trigonometry and write the software tools to help me do the math exercises. Instead of just the old pen and paper, I’d like to make use of a LaTeX engine and parser to enable me to solve these problems like I’d do on paper, but onscreen instead. I think of it basically as a way to generate problem sets and grade them on the fly to get feedback quicker (and to offset the tedium of interacting with the computer using an interface – a keyboard and maybe the mouse – that doesn’t allow easy math symbol input).

Much as I’d like to reprise Vance in its’ entirety, I’ll need to use a University course outline to guide the structure of my application. There were bits of Vance that led into complex analysis, real analysis, and linear algebra that I’d like to include as part of my course flow. I’m imagining an interactive Vance that does for algebra and trigonometry what Push Pop Press did for Al Gore’s book on the environment, and digital media should be able to be molded to the purpose: Javascript and HTML5 have evolved quite a bit since 1996, and might just enable a Web interactive application to do just  that.

Can’t wait to start on elementary physics, a la Angry Birds.

Setting up

I’ve ripped apart my copy of Wylie and Barrett’s Advanced Engineering Mathematics in nice signature-length sections, and have turned it’s first four chapters into nice iPad albums. Ditto for Harry Lass’s Vector and Tensor Analysis.

Over the next four weeks I’ll find either that I’d just wasted eight hours (and one perfectly good copy of W&B) of my previous weekend, or that I can still recover my old maths chops and get on with writing my own MRI scan image synthesis library.