Course Objectives for MAT 1235: Calculus II
This second course in calculus emphasizes integral calculus of functions
of one variable. The primary aims of the course are to help
students develop new problem solving and critical reasoning skills and to
prepare them for further study in mathematics, the physical sciences, or
engineering. By the end of the course, students should be able to:

evaluate definite and
indefinite integrals;

interpret definite
integrals as accumulations of rates of change and as Riemann sums;

explain and apply the Fundamental Theorem of
Calculus;

recognize the difference between definite
and indefinite integrals;

apply integration to
several types of physical problems;

differentiate,
integrate, and solve problems with exponential, logarithmic, and inverse
trigonometric functions;

compute complicated
integrals using a combination of substitutions, algebraic and
trigonometric manipulation, partial fractions, and parts;

recognize and compute
improper integrals;

compute areas,
volumes, and arc
lengths;

recognize and solve some basic differential
equations, including separable equations, logistic equations, and first
order linear equations;

use Maple effectively to explore and solve calculus problems;

analyze and solve complex problems; and

provide
clear written explanations of the ideas behind key concepts from the
course.
Students should also gain an increased
appreciation of mathematics as part of the language of science and as a
study in itself.
Course
Content
The standard
material to be covered in Calculus II from the 6th edition of Stewart's
Calculus is listed below. Individual instructors may make minor
modifications to this list.

5.1 Areas & Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals & the Net
Change Theorem

5.5 The Substitution Rule

6.1 Areas Between Curves

6.2 Volumes

Other instructor selected applications
from chapter 6

7.1 Inverse Functions

7.2* The Natural Logarithmic Function

7.3* The Natural Exponential Function

7.4* General Logarithmic and Exponential
Functions

7.5 Exponential Growth and Decay

7.6 Inverse Trigonometric Functions

7.7 Hyperbolic Functions

7.8 Indeterminate Forms and L’Hospital’s
Rule

8.1 Integration by Parts

8.2 Trigonometric Integrals

8.3 Trigonometric Substitution

8.4 Integration of Rational Functions by
Partial Fractions

8.5 Strategy for Integration

8.6 Integration using Tables and CAS

8.7 Approximate Integration

8.8 Improper Integrals

9.1 Arc Length

Other instructor selected applications
from chapter 9

10.1 Modeling with Differential
Equations

10.2 Direction Fields and Euler's Method

10.3 Separable Equations

10.4 Models for Population Growth

10.5 Linear Equations
