This course expands on the ideas of differential calculus introduced in MATH 185 to techniques of integration and applications of integration. The student successfully completing this course will be able to combine analytic, graphical, numerical, and algebraic methods to solve problems involving integration and power series. The ACU course catalog describes the course as follows:
MATH 186: Calculus II (3-0-3), fall, spring, Continuation of MATH 185. Techniques for finding antiderivatives, applications of integration including volumes of solids of revolution, arc length, and center of mass. Sequences, infinite series, and polynomial approximation. Prerequisites: MATH 185.
Success in Calculus II depends, to a large extent, on knowledge of the mathematics that precedes this course: differential calculus, algebra, geometry, a knowledge of functions and graphing, and trigonometry all play an important role in the course. The following ares are a few of the pre-supposed competencies for this course.
- Use the derivative to analyze where a function is increasing or decreasing, changing concavity, and has maxima/minima. You should be able to algebraically solve for zeros and intercepts of functions, and understand their graphical significance.
- Simplifying rational expressions and expressions involving roots, exponents, exponentials, and logarithms.
- Be able to factor quadratic polynomials and solve for zeros of quadratics using the quadratic formula. Understand the role the discriminant plays in determining the type (real, repeated, complex) of zeros produced.
- Calculate derivatives and differentials of a variety of functions including trigonometric functions.
- Understand the geometric interpretation of the derivative involving slopes, tangent lines. Be able to apply the product, quotient, and chain rules for differentiation.
- Know basic geometric formulas for area, volume, and surface area of common figures like squares, right triangles, circles, and their three dimensional solids.
- Know the interpretation of the definite integral as net area under the curve, and understand the idea of a sum of rectangles approximating the integral. These sums are called Riemann sums.
Calculus II Topics List
Techniques of Integration
- Filling in the Gaps: A First Review
- Substitution Rule
- Integration by Parts
- Trigonometric Integration
- Numeric Integration
- Limits at Infinity
Applications of Integration
- Calculating Areas
- Volumes of Revolution
- Arc Length and Surface Area
- Applications to Physics
- Introduction to Differential Equations
Infinity and Convergence