# MATH 1200: Calculus for Scientists I

- Page ID
- 4145

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

This course provides an introduction to calculus with exposure to applications in science, business, and economics. The main concepts covered are limits, derivatives, and integrals. Derivatives of exponential, logarithmic, trigonometric and inverse trigonometric functions are used to solve optimization, linear approximation, and related rates problems. Techniques of integration and applications are also introduced. Studying calculus will expose students to a variety of important mathematical ideas and help students develop their calculation, critical thinking and problem solving skills.

**This class notes is currently under construction. Please be patient with me.**

- 1: Limit and Continuity of Functions
- 1.0: Library of functions
- 1.1: Introduction to concept of a limit
- 1.2: One sided Limits and Vertical Asymptotes
- 1.3: Limit calculations for algebraic expressions
- 1.4: Limits at Infinity and Horizontal Asymptotes
- 1.5: Formal Definition of a Limit (optional)
- 1.6: Continuity and the Intermediate Value Theorem
- 1.7: Limit of Trigonometric functions
- 1.8: Limits and continuity of Inverse Trigonometric functions
- 1.9: Limit of Exponential Functions and Logarithmic Functions
- 1E: Review Exercises

- 2: Derivatives
- 2.0: Tangent lines and Rates of change
- 2.1: Derivative as a Function
- 2.2: Techniques of differentiation
- 2.3: Derivative as a rate of Change
- 2.4: Derivatives of Trigonometric functions
- 2.5: Chain Rule
- 2.6: Implicit Differentiation
- 2.7: Derivatives of Inverse Trigonometric Functions
- 2.8: Derivatives of Exponential and Logarithmic functions
- 2.9: L'Hôpital's Rule
- 2E: Exercises

- 3: Applications of Derivatives
- 3.0 Introduction to applications of Derivative
- 3.1: Related Rates
- 3.2 Linear approximations and Differentials
- 3.3: Extremas
- 3.4 The Mean Value Theorem
- 3.5 Derivative tests
- 3.6: Applied Optimization Problems
- 3.7: Curve skectching
- 3.8: Newton's Method
- 3.9: Anti derivatives and Rectilinear Motion
- 3E: Chapter Exercises

- 4: Integral Calculus
- 4.0: Antidervatives and Indefinite Integration (Revisited)
- 4.1: Integration by Substitution
- 4.2: Definite Integral- An Introduction
- 4.3: Approximating Areas
- 4.4: The Definite Integral
- 4.5: The Fundamental Theorem of Calculus
- 4.6: Integration Formulas and the Net Change Theorem
- 4.7: Definite integrals by substitution.
- 4.8: Area between two curves
- 4.9: Applications of definite integrals
- 4E: Exercises