# Mathematics 100, Section 102

NOTE: This web page will be updated several times during the term.

Last update: 17:00 3 September 2004

 Topic; Textbook Sections Hrs Topics 1. Limits and Continuity 2.1-2.4 (Appendix M, 1.1-1.5 for background) 5 Tangent lines Limits Limit laws One sided limits, infinite limits, limits at infinity Continuity, Intermediate Value Property 2. Derivatives 3.1-3.4, 3.7 4 Definition of derivative Basic differentiation rules Differentiability implies continuity Vertical tangents Basic trigonometric limit Derivatives of trigonometric functions Chain Rule Simple harmonic motion Particle in a box 3. Exponential, Logarithmic and Inverse Functions, and Applications 3.8, 6.8, part of 8.1, part of 8.3 6 Exponential functions Natural logarithm function Inverse functions Logarithmic differentiation Exponential growth and decay (population growth, radioactivity, chemical kinetics) Linear (nonhomogeneous) equations (heating and cooling, damped motion) Inverse trigonometric functions 4. Some Applications of the Derivative 3.5-3.6, 3.9, 4.3-4.7 14 Maxima and minima of functions on closed intervals Applied maximum-minimum problems Implicit differentiation Related rates Increasing and decreasing functions Mean Value Theorem and consequences First derivative test Curve sketching I Concavity, second derivative Asymptotes Curve sketching II 5. Linear Approximations, Taylor Series and Newton's Method 4.2, 10.4, part of 3.10 4 Linear approximation Taylor polynomials Taylor series Taylor's formula Error in linear approximation Newton's method

#### Textbook

Edwards and Penney, Single Variable Calculus 6e: Early Transcendentals, Prentice-Hall, 2002, with photocopied supplemental material (by Adams, and by Varberg & Fleming) in shrinkwrapped package, to be used in Math 101.

#### Suggested Textbook Problems (not graded - do not hand in)

• See course webpage http://www.math.ubc.ca/~gupta/m100_common

#### Midterm Tests

• Midterm Test 1: Monday, October 4, 12:00-12:50 pm in room BUCH A100
• Midterm Test 2: Monday, October 25, 12:00-12:50 pm in room BUCH A100
• Midterm Test 3: Monday, November 15, 12:00-12:50 pm in room BUCH A100

CALCULATORS ARE NOT ALLOWED.

#### Final Examination

REMEMBER TO BRING PHOTO I.D.

CALCULATORS ARE NOT ALLOWED.

• 20% - Highest of the 3 Midterm marks
• 15% - Lowest 2 of the 3 Midterm marks
• 50% - Final Examination

TERM MARKS WILL BE SCALED TO THE SECTION'S FINAL EXAMINATION AVERAGE.

#### Instructor Information

Instructor: John MacDonald
Email: johnm@math.ubc.ca
Instructor URL: http://www.math.ubc.ca/~johnm
Course URL: http://www.math.ubc.ca/~gupta/m100_common
Office: MATX 1216
Office hours: M W F 2:00 - 2:50 pm, or by appointment
Phone: 604-822-5004