Overarching Goals

As a result of your efforts in this course, you should strengthen your skills in:

• Critical and Creative Thinking
• Problem Solving
• Communication
• Questioning, Problem Posing, and Conjecturing
• Working Collaboratively

Central Theme

The central theme to this course concerns the various ways we can construct a function that satisfies certain prescribed conditions. An example, which is a little beyond the scope of the course, is the problem of constructing an automobile profile (the profile is the function) subject to constraints involving wind drag, style, roominess, etc. An example that you've seen before is to construct a function whose derivative function is sin x and which also has the value 3 when x is 0. A tool that we'll use over and over in Calculus II are ideas of "infinity." For example, we'll try to add up an infinite number of numbers, evaluate an improper integral whose upper limit of integration is infinity, divide an interval into an infinite number of parts, talk about a sequence approaching infinity, express a function as a sum of infinitely many "simpler" functions, and even say that the sum of a series equals infinity.

Chapters/Topics

Chapter 11.1 - 11.7 Infinite Sequences and Series

Chapter 5 Selected Topics concerning the Definite Integral & Fundamental Theorem of Calculus, with emphasis on the definition of integral as a limit of Riemann Sums and the Substitution Rule

Chapter 7 Selected Techniques of Integration, including Integration by Parts and the Method of Partial Fractions

Chapters 6 & 8 Applications of the Definite Integral: Average Value, Probability & Statistics, Economic and Biological Applications

Chapter 11.8 - 11.10 Power Series, Taylor Polynomials and Taylor Series

Chapter 9 Selected Topics in Differential Equations, including Separable Differential Equations and Power Series Methods

Fourier Series - Handout