MATH 101, Winter 2008-9

General information for all sections of Math 101

COURSE OUTLINE

All lecture sections of MATH 101 cover the topics listed below, but may do so in a different order. A “Week” represents approximately a week’s worth of lecture time, not necessarily a calendar week.

Section numbers below refer to the text; most of Chapters 5, 6 and 7 are covered, as well as parts of Chapters 8 and 9 and the Course Notes, which will be made available online. Students should be aware that the course content has changed slightly from previous years. Chapter 17 is no longer part of the syllabus, and more parts of Chapter 9 are covered than previously.

There will be a common final exam for all sections, at a time and place to be announced.

• Week 1
  • §5.1 Areas and Distances
  • §5.2 The Definite Integral (Riemann Sums)
• Week 2
  • §5.3 The Fundamental Theorem of Calculus
  • §5.4 Indefinite Integrals and the Net Change Theorem
  • §5.5 The Substitution Rule
• Week 3
  • §6.1 Areas Between Curves
  • §6.2 Volumes
• Week 4
  • §6.3 Volumes by Cylindrical Shells
  • §6.4 Work
  • §6.5 Average Value of a Function
• Week 5
  • §7.1 Integration by Parts
  • §7.2 Trigonometric Integrals
• Week 6
  • §7.3 Trigonometric Substitution
  • §7.4 Integration of Rational Functions by Partial Fractions
  • §7.5 Strategy for Integration
• Week 7
  • §7.7 Approximate Integration
  • Course Notes §4 Integration Using Taylor Series
• Week 8
  • §7.8 Improper Integrals
  • §8.1 Arc Length
• Week 9
  • §8.3 Applications to Physics and Engineering (Pressure, Force, Centres of Mass)
  • §8.5 Probability (Continuous Random Variables)
• Week 10
  • §9.1 Modeling with Differential Equations
  • §9.2 Direction Fields and Euler's Method
• Week 11
  • §9.3 Separable Equations
  • §9.4 Models for Population Growth
• Week 12
  • §9.5 Linear Equations
  • §Review and Further Applications

UBC Calendar Description: The definite integral, integration techniques, applications, modeling, linear ODEs.

Text: Single Variable Calculus, Early Transcendentals, 6th edition or Calculus, Early Transcendentals, 6th edition, both by James Stewart

Note 1: There are two versions of this textbook. The first one covers single-variable calculus only. The second one, which is larger, covers single-variable, multivariable, and vector calculus. Both versions include all the material needed for MATH 100, 180, and 101.

Note 2: You may be able to use the Option 2 version in follow-up UBC MATH second- and third-year multivariable- and vector-calculus courses (MATH 200, 217, 226, 227, 253, 263, and 317), depending on future textbook adoptions for these courses. Decisions on textbook adoptions for these courses in 2009W will be made in the spring of 2009.

Note 3: Students may be able to purchase second-hand copies of the "Custom editions" of Stewart (6th edition), which were used last year at UBC. This is an acceptable alternative.

Suggested homework problems