Math 1: Calculus with Algebra

Last updated August 28, 2015

Syllabus

The following is a tentative syllabus for the course. The textbook section listed for each day is the one that we intend to cover that day, and it should be read before coming to class.

Lectures
Section In Text
Brief Description
Appendices A-C Review of some topics in precalculus
9/16 1.1 Functions, operations on functions, sequences
9/18 1.1 Graphs of functions, even and odd functions, types of sequences
9/21 1.2, 1.4 Catalogue of functions, average rate of change of a function
9/22 (x-hour) Quiz 1
9/23 1.2 Modeling with functions, Lagrange interpolation
9/25 1.3 Geometric interpretation of function composition
9/28 6.1, 6.2*-6.4* Inverse functions, exponential functions, and logarithmic functions
9/29 (x-hour) Quiz 2
9/30 Appendix D Trigonometric functions
10/2 6.6 Inverse trigonometric functions, solving trigonometric expressions
10/5 11.1 (Informal) limits and convergence of sequences
10/6 (x-hour) Review
10/7 11.1 (Formal) limits of sequences
10/8 Exam 1
10/9 11.1 More on convergent sequences
10/12 1.5 (Informal) limits of functions, limits at infinity, asymptotes
10/13 (x-hour) Quiz 3
10/14 1.6, 1.7 (Formal) limits of functions, properties of limits
10/16 1.8 Continuous functions
10/19 1.6, 1.8 Squeeze Theorem, limits and continuity of trigonometric, exponential, and logarithmic functions
10/20 (x-hour) Quiz 4
10/21 1.4, 2.1 Rates of change and the derivative, tangent lines
10/23 2.2 The derivative as a function
10/24 (Saturday class) 2.3, 6.2 Derivative rules
10/26 2.3 Product and Quotient Rules, higher order derivatives
10/27 (x-hour) Review
10/28 2.4 Derivatives of trigonometric functions
10/29 Exam 2
10/30 6.4 Derivatives of exponential and logarithmic functions
11/2 2.5 Chain Rule
11/3 (x-hour) Quiz 5
11/4 2.6, 6.6 Implicit differentiation, derivatives of inverse trigonometric functions
11/6 6.8 L'Hospital's Rule
11/9 3.8 Newton's Method
11/10 (x-hour) Quiz 6
11/11 2.9 Linear approximation
11/13 2.9, 11.10 Taylor polynomials
11/16 11.11 Approximation using Taylor polynomials
11/17 (x-hour) Review/wrap-up
11/20 Final exam