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Sep 17, 2024
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# MATH& 152 Calculus II (5 credits)

Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 125 - CCN

Prerequisite MATH& 151  with a grade of 2.0 or higher or instructor permission.

Course Description
Fundamental Theorem of Calculus. Definite and indefinite integrals. Methods of Integration. Applications of integration. Improper integrals. Introduction to first order differential equations.

Student Outcomes
Techniques and Concepts of Integration
1. Apply the following techniques of integration to integrate polynomial, rational, and transcendental functions without use of technology: Power rule, substitution, parts, partial fractions, and algebraic manipulation.
2. Evaluate definite integrals graphically and with the Fundamental Theorem of Calculus.
3. Apply the Fundamental Theorem of Calculus to find the derivative of integral functions.
4. Identify and evaluate improper integrals.
5. Apply approximation techniques (such as Riemann sums, trapezoidal rule, Simpson’s rule) in order to approximate the value of definite integrals, and evaluate the accuracy of their answer using error formulas or other methods.

Applications of Integration
6. Compute the area under a curve and between curves using integration and interpret the solution in the context of the problem.
7. Compute volumes of solids of revolution and other solids using disc, washer, shell and cross-section integration techniques.
8. Calculate the length of a curve using integration.
9. Calculate the average value of a function using integration.
10. Apply integrals to solve a variety of problems in physics, engineering, economics, chemistry, or biology.

Differential Equations
11. Sketch and interpret direction fields.
12. Match graphical solutions to differential equations.
13. Solve and sketch solutions to ordinary, first-order differential equations for multiple initial conditions using numerical or graphical techniques.
14. Solve separable differential equations analytically.

General Content
15. Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation, units, and appropriate language.
16. Solve and analyze application problems that involve concepts covered in this course and in previous courses.
17. Use technology appropriately as a tool to solve problems.
18. Link graphical, numeric, and symbolic representations of the integral when interpreting situations and analyzing problems.

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