Syllabus

Science Prerequisites for Health Professionals

MATH 1020: Calculus I – Summer Session 2023 – 6 weeks

Credits - 4

Description

This course focuses on single variable calculus through graphical, analytical, and numerical techniques. Differentiation and its applications are thoroughly discussed. Basic integration techniques are introduced. Mathematical manipulation and computational competence is equally weighted with the ability to analyze, evaluate, synthesize and form accurate decisions using relevant information in applied settings.

Prerequisite Knowledge

Mastery of algebra and trigonometry is assumed in this course, as well as general mathematical problem solving. Without the use of technology, students are expected to demonstrate proper mathematical notation, definitions, and algebraic manipulation of the following types of functions: polynomial, rational, exponential, logarithmic, sinusoidal and their inverses.

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 1.
   1. Limits and Continuity: Graphical interpretation, numerical approximation, limit laws, Squeeze Theorem, Intermediate Value Theorem, tangent and velocity problems, L’Hopital’s rule
   2. Derivatives: Formal definition of a derivative, Delta – Epsilon proofs, differentiation rules, trig formulas, chain, product and quotient rules, implicit and logarithmic differentiation 
   3. Applications of the derivative: Rates of change, related rates, Mean Value Theorem. curve sketching, local and absolute extrema, optimization, linear approximations, Newton’s method.
   4. Integrals: Approximating areas, antidifferentiation, Riemann sums, Fundamental Theorem of Calculus, definite and indefinite integrals, substitution methods
   5. Applications of Integration: Area under and between curves, volumes of revolutions, arc length, work, hydrostatic force, moments and centers of mass, exponential growth and decay models, hyperbolic functions
2. Utilize numerical, graphical, analytical and approximation models in pure and applied settings.
3. Communicate mathematical concepts and apply complex symbolic representation in written, verbal, and technological settings.
4. Develop the ability to identify and apply multiple mathematical problem-solving techniques for a specific situation.

Assignments

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 (3)

There will be a total of three 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.  The midterm exam covers material from Weeks 1-3 of the course. A practice midterm exam will be available to help students study. This exam must be taken with the Respondus Lockdown Browser.

Final Exam

A final exam will take place in WebAssign at week six.  This exam will cover material from Weeks 4-6. A practice exam will be available to help students study. This exam must be taken with the Respondus Lockdown Browser. 

Grading Policy

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

Grade Breakdown