(old) SIM 1002, SJEM 1111 - Calculus 1, Semester 2, session 2017-18

(old) Lectures


Tuesdays, 2-4 pm in DKM2
Thursdays, 2-4 pm in DKM2

Tutorial class schedule

To be decided...

Course textbook

The textbook used is Thomas' Calculus, 14th Edition, Global Edition, by George B. Thomas, Maurice D. Weir, Joel R. Hass, published by Pearson Education, Inc.



Course contents


Week 1: Functions and graphs.
Section 1.1: Functions and their graphs

Week 2: Combining functions, trigonometric functions.
Section 1.2: Combining functions
Section 1.3: Trigonometric functions

Week 3: Rates of change and limit. Limit theorems. The precise definition of a limit.
Section 2.1 Rates of change and tangent lines to curves
Section 2.2 Limit of a function and limit laws
Section 2.3 The precise definition of a limit

Week 4: One-sided limit. Continuity. Limits involving infinity. Asymptotes of graphs.
Section 2.4: One-sided limits
Section 2.5 Continuity
Section 2.6 Limits involving infinity; Asymptotes of graphs

Week 5: Tangent lines and the derivative at a point. The derivative as a function.
Section 3.1: Tangent lines and the derivative at a point
Section 3.2: The derivative as a function

Week 6: Differentiation rules. Derivative of trigonometric functions. TEST 1.
Section 3.3: Differentiation rules
Section 3.5: Derivatives of trigonometric functions

Week 7: The chain rule. Implicit differentiation.
Section 3.6: The chain rule
Section 3.7: Implicit differentiation

Week 8: Extreme values of functions on closed intervals
Section 4.1: Extreme values of functions on closed intervals

Week 9: The mean value theorem. Monotonic functions and the first derivative test
Section 4.2: The mean value theorem
Section 4.3: Monotonic functions and the first derivative test

Week 10: Concavity and curve sketching. Antiderivatives.
Section 4.4: Concavity and curve sketching

Week 11: Sigma notation and limits of finite sums
Section 5.2: Sigma notation and limits of finite sums

Week 12: The definite integral. The fundamental theorem of Calculus
Section 5.3: The definite integral
Section 5.4: The fundamental theorem of calculus

Week 13: Indefinite integrals and the substitution method. TEST 2.
Section 5.5: Indefinite integrals and the substitution method

Week 14: Revision.