SPU Mathematics

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;

• 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; and

• use Maple to effectively to explore and solve calculus problems.

In addition to the specific skill-oriented objectives above, students should

• understand definite integrals as accumulations of a rate of change and as Riemann sums;

• understand the relationship between derivatives and integrals;

• understand the difference between definite and indefinite integrals;

• have improved skills at problem solving and critical thinking: at dissecting a complex problem, determining steps in its solution, finding the solution, and testing whether it is reasonable; and

• be able to 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