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Calculus

Vak 2013-2014

Tag(s)

[Bsc], S, PSc, GPH

Admission Requirements

None.

Description

This course is an intensive introduction to the calculus of elementary functions and its applications to science, economics, and statistics. We will begin with the fundamental concepts of limits, continuity, and derivatives, and explore the derivatives and integrals of polynomials, rational functions, exponentials, logarithms, and trigonometric functions. Students will learn to differentiate composite functions using the chain rule, logarithmic differentiation, and other tools, as well as techniques for integration such as integration by substitution or integration by parts. In the later weeks of the course, we will explore derivatives of multivariate functions of multiple variables, problems of extremization, and model exponential growth, sinusoidal oscillation, and logistic convergence through simple differential equations.

Course Objectives

Students will:

  • engage interactively with course content in class,
  • understand the integral and differential calculus of elementary functions and their applications,
  • clearly express their understanding in writing, and
  • synthesize the concepts they learn and apply them in combination

Mode of Instruction

In this class, students will primarily learn material through group discussion, where we explore concepts and phenomena by asking questions and discovering the answers together. In addition, students will receive instant feedback in class to check their understanding and guide the lecture portions of class time. We will use computer simulations to explore real-life behaviors and their mathematical underpinnings, and students will cement their understanding through weekly assignments.

Assessment

Assessment: In-class participation
Learning aim: Interactive engagement with course material
Percentage: 20%
Deadline: Ongoing Weeks 1 – 7

Assessment: Weekly quizzes
Learning aim: Understanding of course content
Percentage: 20%
Deadline: Weeks 1 – 7 (Friday at 15:00)

Assessment: Weekly take-home assignments
Learning aim: Clear expression of learned concepts
Percentage: 30%
Deadline: Weeks 2 – 7 (Tuesday at 17:00)

Assessment: Take-home final exam
Learning aim: Holistic understanding of course material
Percentage: 30%
Deadline: Week 8 (Friday at 15:00)

Literature

None.

Contact Information

Contact information will be provided on the first day of class.

Weekly Overview

Week 1: Limits, Continuity, and Derivatives
Week 2: Integrals and Derivatives of Elementary Functions
Week 3: The Chain Rule and Integration by Substitution
Week 4: Multivariate Functions and Partial Derivatives
Week 5: Maximization and Minimization
Week 6: Exponential Growth; Differential Equations
Week 7: Oscillatory Behavior and Special Topics
Week 8: Reading Week

Preparation for first session

None.