## MATH 105 - Calculus for Social and Biological Sciences I

This introductory course to calculus emphasizes on applications rather than theory. Topics include: derivatives and rates of growth; exponential and circular functions; differentials, chain rule; implicit differentiation; maxima and minima; curve sketching; differention and maximum-minimum problems for functions of several variables.

Credits: 3

Hours: 60 (Lecture Hours: 3; Seminars and Tutorials: 1)

Total Weeks: 15

Prerequisites:
Math 12 or equivalent.

Non-Course Prerequisites:
None

Co-Requisites:
None

Course Content:
FUNCTIONS AND GRAPHS
- Introduction to Functions.
- Graphing Functions.
- Linear Functions and Applications.
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
LIMITS AND AN INTRODUCTION TO THE DERIVATIVE.
- An Introduction to Limits.
- Limits at Infinity and Infinite Limits - Asymptotes.
- Continuity.
- Rate of Change and Slope
- The Tangent Line to a Curve
- The Derivative
THE DERIVATIVE
- Basic Differentiation Formulas.
- The Chain Rule.
- Higher Derivatives.
- Implicit Differentiation.
- Related Rates.
- Differentials.
APPLICATIONS OF THE DERIVATIVE
- Increasing and Decreasing Functions.
- Finding Maxima and Minima: The First Derivative Test.
- Concavity, Point and Inflection, and the Second Derivative Test.
- Absolute Maxima and Minima.
- Curve Sketching.
- Optimization Problems.
TRIGONOMETRIC FUNCTIONS
- Trigonometric Functions Review
- Differentiation of Trigonometric Functions
INTEGRATIONS
- Antiderivatives and Indefinite Integrals.
- Integration by Substitution.

Learning Outcomes: On successful completion of this course, the student will be able to:
- Calculate limits.
- Differentiate polynomial, exponential, logarithmic, and trigonometric functions.
- Apply differentiation to curve sketching, related rates, maxima and minima.
- Learn to integrate indefinite integrals using substitution.