Math 3152 Calculus II

  1. Course Philosophy
  2. Generic Course Objectives
  3. Classroom Behaviour
  4. On the use of electronic aparati
  5. Recomendaciones para Estudiantes Nuevos
  6. In Praise of Lectures
Week  Topics
1Review
2 Transcendental Functions
3 Integration by Parts
4 Hyperbolic Functions and selectd Applications
5 Rational Functions, Improper Integrals
Exam I 
6Differential Equations and transcendental functions.
7Sequences and Series
8-9Convergence of Series
10Power Series, Taylor Polynomials
Exam 2
11 Conic Sections
12-13 Conic Sections and Parametrized Curves
14 Arclength and Curvature
Exam 3
15 Polar Coodinates
Exam IV  

Topic 1. Review of Calculus 1

  1. Chain rule
  2. Definition of the integral 
  3. The fundamental theorem of calculus.

Topic 2. Transcendental Functions – Continued

  1. The derivative of the logarithm function – geometric version   
  2. The logarithm and exponential functions using the Fundamental Theorem of Calculus,

Topic 3. Integration by Parts

  1. Integration by parts
  2. Trigonometrical Function.  
  3. Integrals involving the Secant Function

Topic 4. Hyperbolic functions and some applications

  1. Trigonometrical and Hyperbolic Functions – A Comparison
  2. Hyperbolic Functions.

Topic 5. Rational Functions, Improper Integrals

  1. Rational Functions
  2. Integration of Rational Functions
  3. Improper Integrals

Topic 6. Differential Equations and Transcendental Functions

  1. Introduction to ODE’s
  2. Terminal Velocity

Topic 7. Sequences and Series

  1. Review Calculus I material on Sequences

Topics 8-9 . Convergence of Series

  1. Convergence of Series.
  2. Power Series

Topic 11. Conic Secions

Topics 12-13 Conic Sections and Parametrized Curves

Topic 14 Arclength and Curvature

  1. Curvature in 2 dimensions
  2. The Cycloid

Topic 15. Polar Coordinates

  1. Polar Coordinates

Supplementary Notes

  1. Some Ways to Define Functions
  2. Remarks on Parity
  3. Exponential Series
  4. Limit Superior and Limit Inferior

Practice Exercises

  1. Limits of Sequences (Calculus I)
  2. Limits of Sequences (Calculus II)
  3. Limits of Functions (Calculus I)
  4. Indeterminate Forms
  5. Definite Integrals (Calculus I)
  6. Integration by Parts
  7. Trignometric Functions
  8. Ordinary Differential Equations
  9. Integrals (Calculus II)
  10. Polar Coordinates

Text

George B. Thomas Jr. Maurice D. Weir, and Joel R. Hass, Calculus, 12th Edition.

Bibliography

  1. K. Kodaira, (Editor), Basic Analysis, Japanese Grade 11. AMS
  2. Y. M. Chow et. al., College Mathematics Volume 2, Syllabus C, Pan Pacific Publications, ISBN 9971-63-863-0.
  3. Stewart and Tall, Foundations of Mathematics, Ed. 1, Oxford University Press.
  4. Serge Lang, A First Course in Calculus, Addison Wesely, 1968.
  5. Serge Lang, A Second Course in Calculus, Addison Wesely, 1968.
  6. Salas, Hille y Anderson, Calculus, One and Several Variables, John Wiley.
  7. Lecture Notes
  8. (Free) Precalculus Book by David Santos
  9. (Free) Ossifrage-And-Algebra-2007 by David Santos
  10. (Free) Pre-y Cálculo Criollos (Spanish Version) by David Santos
  11. (Free) Andragogic Propaedeutic Mathematics by David Santos
  12. (Free) The Elements of Infinitesimal Calculus by David Santos
  13. Michael Spivak, Calculus, Publish or Perish Inc., 1968.

Practice Exams

  1. Practice Exam I


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