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:<\/p>\n
MATH 186: \u00a0Calculus II (3-0-3), fall, spring, \u00a0Continuation of MATH 185. \u00a0Techniques for finding antiderivatives, applications of integration including volumes of solids of revolution, arc length, and center of mass. \u00a0Sequences, infinite series, and polynomial approximation. \u00a0Prerequisites: \u00a0MATH 185.<\/p><\/blockquote>\n
Success in Calculus II depends, to a large extent, on knowledge of the mathematics that precedes this course: \u00a0differential calculus, algebra, geometry, a knowledge of functions and graphing, and trigonometry all play an important role in the course. \u00a0The following ares are a few of the pre-supposed competencies for this course.<\/p>\n
\n
- Use the derivative to analyze where a function is increasing or decreasing, changing concavity, and has maxima\/minima. \u00a0You should be able to algebraically solve for zeros and intercepts of functions, and understand their graphical significance.<\/li>\n
- Simplifying rational expressions and expressions involving roots, exponents, exponentials, and logarithms.<\/li>\n
- Be able to factor quadratic polynomials and solve for zeros of quadratics using the quadratic formula. \u00a0Understand the role the discriminant plays in determining the type (real, repeated, complex) of zeros produced.<\/li>\n
- Calculate derivatives and differentials of a variety of \u00a0functions including trigonometric functions.<\/li>\n
- Understand the geometric interpretation of the derivative involving slopes, tangent lines. \u00a0Be able to apply the product, quotient, and chain rules for differentiation.<\/li>\n
- Know basic geometric formulas for area, volume, and surface area of common figures like squares, right triangles, circles, and their three dimensional solids.<\/li>\n
- 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. \u00a0These sums are called Riemann sums.<\/li>\n<\/ul>\n
The course is divided into three units: techniques of integration, applications of integration, and infinity and convergence. \u00a0The links below will take you to individual pages for each of the topics within these units. \u00a0Most pages contain lecture notes, videos, or other resources to assist you in learning the material.<\/div>\n<\/p>\n
<\/p>\n
Calculus II Topics List<\/h1>\n
<\/p>\n
<\/h2>\n
Techniques of Integration<\/h2>\n
\n
- Filling in the Gaps: \u00a0A First Review<\/a><\/li>\n
- Substitution Rule<\/a><\/li>\n
- Integration by Parts<\/a><\/li>\n
- Trigonometric Integration<\/a><\/li>\n
- Numeric Integration<\/a><\/li>\n
- Limits at Infinity<\/a><\/li>\n<\/ul>\n
<\/p>\n
Applications of Integration<\/h2>\n
\n
- Calculating Areas<\/a><\/li>\n
- Volumes of Revolution<\/a><\/li>\n
- Arc Length and Surface Area<\/a><\/li>\n
- Applications to Physics<\/a><\/li>\n
- Introduction to Differential Equations<\/a><\/li>\n<\/ul>\n
<\/p>\n
Infinity and Convergence<\/h2>\n
\n
- Sequences and Series<\/a><\/li>\n
- Convergence Tests<\/a><\/li>\n
- Power Series<\/a><\/li>\n
- Taylor Series<\/a><\/li>\n
- Binomial and Fourier Series<\/a><\/li>\n<\/ul>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
This course expands on the ideas of differential calculus introduced in MATH 185 to techniques of integration…<\/p>\n","protected":false},"author":130,"featured_media":189,"parent":117,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-96","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/96","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/users\/130"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/comments?post=96"}],"version-history":[{"count":43,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/96\/revisions"}],"predecessor-version":[{"id":1087,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/96\/revisions\/1087"}],"up":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/117"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/media\/189"}],"wp:attachment":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/media?parent=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}