Math 1211 Calculus

MATH 1211: Calculus

Course Description:

This 3-credit course provides an interdisciplinary introduction to the core concepts of differential calculus, covering a wide range of topics. Content includes both applications and theory of differential calculus leading to an introduction of The Fundamental Theorem of Calculus. Learners will continue to refine independent study skills, problem-solving, logically correct and mathematically precise writing and thinking, and their ability to use geometric, symbolic and analytic formats in presenting solutions to both abstract and real-world applications. Class activities will include lecture/discussion as well as tests and quizzes. Students will communicate their results in written form.

Required Textbook and Materials:

The main required textbooks for this course are listed below and can be readily accessed using the provided links. There may be additional required/recommended readings, supplemental materials, or other resources and websites necessary for lessons; these will be provided for you in the course’s General Information and Forums area, and throughout the term via the weekly course Unit areas and the Learning Guides.

Software Requirements/Installation:

No special requirements.

Learning Objectives and Outcomes:

By the end of this course students will be able to:

1. Learn actively by:
   • Integrating technology into problem-solving.
   • Taking responsibility for accessing and using a variety of sources for assistance in learning about calculus,  including its history.
2. Think critically and creatively by:
   • Using deductive and inductive reasoning in applying calculus to real-life situations.
   • Analyzing, contrasting and critiquing various procedures – the “rules” of calculus.
   • Following, evaluating, and writing solutions to mathematical problems, arguments, and proofs.
3. Communicate clearly and originally by:
   • Explaining how answers were created — stating assumptions made and conclusions supported by the analysis.
   • Formulating and criticizing mathematical conjectures and conclusions.
   • Reading and writing mathematical presentations that use mathematical vocabulary, notation, and graphical interpretations.
4. Interact in the diverse and complex environment by:
   • Recognizing the biases and limitations of mathematical models.
   • Respecting individual ways of arriving at answers, expressing results, and processing information.

Course Schedule and Topics:

This course will cover the following topics in eight learning sessions, with one Unit per week. The Final Exam will take place during Week/Unit 9.

Week 1: Unit 1 – Calculus Introduction: Velocity, Circular Motion, Trigonometric Functions

Week 2: Unit 2 – Limits and Derivatives: Rates of Change and Limits and the Derivative of a Function

Week 3: Unit 3 – Derivative Rules, Derivatives of Trigonometric Functions, and Limits and Continuity

Week 4: Unit 4 – Applications of Derivatives, Extreme Values of Functions, and the Mean Value Theorem

Week 5: Unit 5 – The Chain Rule and Implicit Differentiation

Week 6: Unit 6 –Exponential and Logarithmic Functions

Week 7: Unit 7 –Newton’s Method and the Integral and Antiderivative

Week 8: Unit 8 –More on the Integral, Definite Integrals, and Fundamental Theorem of Calculus

Week 9: Unit 9 –Course Review and Final Exam