Syllabus

UNE Summer Session

MATH 1021: Calculus II – 6 Weeks

Credits - 4

Description

This course continues the study of calculus. More techniques of integration will be investigated in this course. The concepts of limits, differentiation, and integration will be applied to problems in differential equations, sequences, series, and Taylor series. Parametric equations, polar coordinates, and vectors will also be introduced. (Calculus 1 is a prerequisite for this course).

Resources Section/Technology

Students will be instructed in utilization of technology.  Online, freely available technology will often be recommended. Student calculations will be submitted via WebAssign mathematical editor for online homework. Students will utilize email and/or Blackboard for written communication.

Prerequisite Knowledge

An understanding of the topics and core concepts in Calculus I is prerequisite knowledge for Calculus II.

Materials

Learning Objectives and Outcomes

By the end of this course, you will be able to:

1. Apply the core concepts of differential and integral calculus to solve problems in Calculus II.
   1. Review of integration:  Area approximation, substitution methods, The Fundamental Theorem of Calculus, exponential, logarithmic, and inverse trigonometric functions.
   2. Advanced integration techniques:  Integration by parts, trigonometric integrals, integration using trigonometric substitution, integration using partial fractions, numerical integration, improper integrals.
   3. Differential equations:  Direction/slope fields, numerical solutions, separable differential equations, first-order linear equations.
   4. Sequences and series:  Introduction to sequences and series, infinite series, tests for convergent series.
   5. Taylor and Maclaurin series: Definition of Taylor and Maclaurin series, power series.
   6. Polar coordinates: Explanation of the polar coordinate system, integration using polar equations, conic sections in polar coordinates.
   7. Parametric equations: Introduction to parametric equations, calculus using parametric curves
   8. Vectors: Introduction to vectors, dot product, cross product, equations of lines and planes in space.
2. Utilize numerical, graphical, analytical and approximation models in pure and applied settings.
3. Develop visual literacy of Calculus II concepts through graphical analysis.
4. Communicate mathematical concepts and apply complex symbolic representation in written, verbal, and technological settings.
5. Develop the ability to identify and apply multiple mathematical problem-solving techniques for a specific situation.
6. Gain further knowledge appropriate to a single variable calculus course of mathematical definitions and proofs of key theorems.

Assignments

Applied Problems

Four applied problems are assigned within Brightspace. You will either type up your solutions in a word or PDF document or take a picture of your hand-written solutions and upload it to Brightspace. 

Homework Problem Sets

Six problem sets are assigned through WebAssign, an online homework tool. The problem sets typically cover problems from three different sections of the text, plus a recap and review section each week. Students can retry problems up to five times if they get questions wrong.

Discussion Boards (4)

There will be a total of four discussion boards in the course.  The discussion boards are designed to encourage students to reflect on their learning process and collaborate with one another on problems in the course that are challenging them. 

Midpoint Exam

A midterm exam will take place in WebAssign at week four.  A practice midterm exam will be available to help students study. Final Exam

A final exam will take place in WebAssign at week six. A practice exam will be available to help students study. 

Grading Policy

Your grade in this course will be determined by the following criteria:

Grade Breakdown