Math 3A: Calculus for Life Sciences

General Information

Time and Place: MWF 12-12:50pm WG Young Hall, CS24

Instructor: Henry Towsner

E-mail address: hpt at math.ucla.edu

Office: Mathematical Sciences Building 5634
Office Phone: (310) 825-2697
Office Hours: W 1:00-3:00, F 10:30-11:30, or by appointment

Course Information

Course Outline

Practice for Midterm 1 and solutions

Solutions to Midterm 1

Practice for Midterm 2 and solutions

More example problems for Midterm 2

Solutions to Midterm 2

Practice Final

Description

This is the first class in the calculus sequence for life science students. We will introduce the central concept of calculus, the derivative. We will study the properties of derivatives, and how to compute them, and then turn to an examination of how we can use the derivative to investigate the behavior of mathematical functions.

Course Text

Neuhauser, Calculus for Biology and Medicine, 3rd Ed, Prentice Hall

Homework

Homework 1, due Mon, Sep. 27th: Read the course information handout
Homework 2, due Mon, Oct. 4th: Section 2.2, Problems 3, 4*, 31, 32*, 41, 42*, 47, 48*, 75, 76* solutions
Homework 3, due Mon, Oct. 11th: Section 3.1, Problems 9, 10*, 21, 22*, 47, 48*
Section 3.2, Problems 11, 12*, 23, 24*, 25b, 26b*, 41, 42*
Section 3.3, Problems 17, 18*, 19, 20*
Give examples of two functions, f(x) and g(x), such that limx→1f(x) does not exist, limx→1g(x) does not exist, but limx→1(f(x)/g(x))=0.* solutions
Homework 4, due Mon, Oct. 18th: Section 3.4, Problems 1b, 2b*, 7, 8*
Section 3.5, Problems 5, 6*, 13, 14*, 15
Section 4.1, Problems 25, 26*, 27, 28*, 51, 52*, 70*
Section 4.2, Problems 7, 8*, 29, 30*, 81, 82*
Section 4.3, Problems 31, 32*, 67, 68*, 84*, 85
Prove, using the definition of the derivative, that (a f(x))'=a f'(x) (where a is constant with respect to x).*
solutions (images for 4.1.70: differentiable, continuous but not differentiable, discontinuous

Homework 5, due Mon, Nov. 1st: Section 4.4, Problems 3, 4*, 15, 16*, 61, 62*, 69, 70*, 75, 76*, 83, 84*
Section 4.5, Problems 5, 6*, 47, 48*, 63, 64*
Section 4.6, Problems 1, 2*, 45, 46*
solutions
Homework 6, due Mon, Nov. 8th: Section 4.6, Problems 61, 62*
Section 4.7, Problems 9, 10*, 22*, 29, 30*, 71, 72*
Section 4.8, Problems 1, 2*, 12*, 13, 46*, 47
Section 5.1, Problems 21, 22*, 31, 32*
solutions

Homework 7, due Mon, Nov. 15th: Section 5.1, Problems 41, 42*, 43, 44*, 46*, 47
Section 5.2, Problems 6*, 7, 8*, 9, 31, 32*
Section 5.3, Problems 2*, 3, 4*, 5, 19, 20*
Draw a function f so that f'(x) is negative when x is negative, f'(x) is positive when x is positive, but f(0) is not a minimum.*
solutions
Homework 8, due Mon, Nov. 29th: Section 5.4, Problems 3, 4*, 12*, 13, 22*, 23
Section 5.5, Problems 7, 8*, 15, 16*, 25, 26*, 27, 28*, 55, 56*
solutions