Applied Calculus II Course of Study

Course title and description: Applied Calculus II: Covers techniques of integration, multivariable calculus and an introduction to differential equations. Prerequisite: MTH 271 or equivalent. Lecture 3 hours per week.

Broad goals: The student will use the concepts of the derivative, the differential and differential equations to relate quantities to rates of change to exponential and logarithmic functions. The student will learn the basic techniques for calculating integrals, and the concepts necessary to apply integration to real-world problems related to the study of business, economics, management, and the social and life sciences.

Specific objectives: Each assigned problem constitutes a specific objective, which is to solve the problem and to use it as a means of synthesizing the student's understanding of the subject. Objectives may be partially categorized as follows:

Understand exponential and logarithmic functions and their derivatives and their applications, and apply the techniques of differentiation to these functions as appropriate.

Know and be able to apply the rules for integrating power functions, polynomials, exponential functions and logarithmic functions.

Know and be able to apply the techniques of integration by substitution and integration by parts.

Be able to apply integration to solving a wide variety of problems involving sums and averages.

Be able to identify and sketch the various quadric surfaces and relate these surfaces to their defining equations.

Know how to find values of functions of two or more variables, and to find partial derivatives and tangent lines for such functions.

Apply the techniques necessary to find relative and absolute maxima and minima for functions of two variables.

Apply the theory of functions of two variables to determine the equations for linear and quadratic regression lines.

Evaluate double integrals and change the order of integration for a given double integral.

Use double integrals to find the areas of region in the plane bounded by given functions.

Instructional methodologies

In-class Students

Concepts will typically be developed within the context of a concrete model, often with hands-on experience to provide a basis on which to develop a deeper and more general understanding of the concept. Concrete and specific examples will be generalized into graphical and symbolic form. Class will typically be divided between lecture and hands-on problem solving, in more or less equal proportions. Lecture notes will be posted on the Internet, and versions of the lecture notes with hyperlinked video lectures will be available in a CD-R format. Students will also need a graphing calculator (any graphing calculator will do) and will be required to learn the rudiments of the computer program DERIVE, which is available on VHCC computers.

Tests and Exams: Four tests and a final exam will be given during the semester. Tests and exams will be generated from a large problem bank and will be administered through the college Learning Lab. Distance students may with instructor approval arrange to take tests and exams in some other acceptable secure and supervised testing environment.

Grading policy: All grades will be normalized to the following scale: 90-100% constitutes an A; 80-90% constitutes a B; 65-80% constitutes a C; 50-65% constitutes a D.

Homework and participation will count as 20% of the final grade.

Tests and final exam will be averaged to comprise the remaining 80% of the final grade; however if it is to the student's advantage the test average and the final exam will each count as 40% of the final grade.

Text: The text for the course is Applied Calculus by Larson and Edwards, latest edition, published by Houghton-Mifflin.

Units to be covered:

Chapters 4-7 inclusive, plus supplementary material posted by instructor.

Chapter Topics:

Chapter 4: Exponential and Logarithmic Functions

Chapter 5: Integration

Chapter 6: Applications of Integration

Chapter 7: Multi-Variable Calculus

Specific information regarding assignments and areas covered is included on the homepage at 164.106.222.236.