MATH 116 Survey of Calculus II

This course is a: Lower Division ES Distance Ed, Major Course, transferIN

Course Outcomes

Upon completion of this course students will be able to:

* Evaluate partial derivatives and multivariate functions.

* Find relative extreme.

* Solve integration problems.

* Apply integration techniques to solve continuous money flow problems.

* Analyze and solve applied problems involving improper integrals.

* Analyze elementary differential equations and geometric series.

* Determine Taylor polynomial of a degree n for a given function.

Course Text and Materials

CALCULUS W/APPLICATIONS-MYLAB ACCESS

9780137342495

Graphing Calculator

Webcam with Microphone

Course Content

Multivariable Calculus

At the completion of this unit, successful students will be able to:

1. Apply the differentiation techniques of MATH 115.

2. Find a function value for a function of several variables.

3. Find the partial derivatives of a given function.

4. Evaluate the partial derivatives of a given function.

5. Find the four second-order partial derivatives of a function.

6. Find the relative maximum and minimum values of a function of two variables.

7. Compute the total differential of a multivariable function of two or more variables.

8. Use the total differential of a multivariable function to approximate actual changes in the function corresponding to changes in the independent variable.

9. Find a maximum or minimum value of a given function subject to a given constraint, using the method of LaGrange multipliers.

10. Analyze and solve applied problems involving LaGrange multipliers.

Integration

At the completion of this unit, successful students will be able to:

1. Apply the integration techniques of MATH 115.

2. Solve integration problems by the technique of integration by parts.

3. Solve various application problems involving integration.

4. Analyze and solve definite integral applications.

5. Find the average value of a function.

6. Use the disk method to find the volume of a solid of revolution.

7. Analyze and solve problems dealing with continuous money flow.

8. Use an integral table.

9. Determine whether an improper integral is convergent or divergent, and

10. Calculate its value if it converges.

11. Analyze and solve applied problems involving improper integrals.

12. Verify that a given function satisfies the property: x)dx = 1 for a given probability density function.

13. Find k such that a function like f(x) = kg(x) is a probability density function over an interval [a, b].

14. Use the Trapezoidal rule and Simpson’s rule for area approximation.

Differential Equations

At the completion of this unit, successful students will be able to:

1. Solve elementary differential equations, giving both general and particular solutions.

2. Solve elementary differential equations given a condition f(a) = b.

3. Verify that a given function is a solution of a given differential equation.

4. Solve certain differential equations using separation of variables.

5. Solve linear first-order differential equations.

6. Analyze and solve applications involving differential equations.

Sequences and Series

At the completion of this unit, successful students will be able to:

1. Use summation notation to write series.

2. Define and calculate nth partial sums of series.

3. Analyze geometric series and find the sum of a convergent geometric series.

4. Determine if a series converges or diverges.

5. Find Taylor polynomials of degree n for given functions and use them to approximate functional values.

6. Find Taylor series and intervals of convergence for given functions.

VU Liberal Education Outcomes met by this course

.  Apply quantitative reasoning and a variety of numeric data to solve problems in a variety of disciplines.

UCC/State Outcomes met by this course

· Quantitative Reasoning

.   3.1. Interpret information that has been presented in mathematical form (e.g. with functions, equations, graphs, diagrams, tables, words, geometric figures).

.   3.2. Represent information/data in mathematical form as appropriate (e.g. with functions, equations, graphs, diagrams, tables, words, geometric figures).

3.3. Demonstrate skill in carrying out mathematical (e.g. algebraic, geometric, logical, statistical) procedures flexibly, accurately, and efficiently to solve problems.

.   3.4. Analyze mathematical arguments, determining whether stated conclusions can be inferred.

.   3.5. Communicate which assumptions have been made in the solution process.

3.6. Analyze mathematical results in order to determine the reasonableness of the solution.

.   3.7. Cite the limitations of the process where applicable.

3.8. Clearly explain the representation, solution, and interpretation of the math problem.