MATH 2914
Lecture Notes

The following are lecture notes designed for the calculus I class at ATU. The topics follow the partition of the textbook "Single and mutlivariable Calculus" by Hughes-Hallett et al. These notes have been improved and will continue to be. Please feel free to browse through them.

To Students: BEWARE! The notes posted here are those that I write for myself to bring to class so that if you miss class, you can see approximately what we covered. I will NOT be posting notes as they would appear in class. There will be many missing examples and explanations. This is not a replacement for coming to class and taking notes yourself.

§ 1.1 Functions and Change
§ 1.2 Exponential Functions
§ 1.3 Building New Functions from Old Ones
§ 1.4 Logarithmic Functions
§ 1.5 Trigonometric Functions
§ 1.6 Polynomial and Rational Functions
§ 2.1 Velocity as a Rate of Change
§ 2.2 The Concept of Limit
§ 1.7 The Concept of Continuity
§ 2.3 The Derivative at a Point
§ 2.4 The Derivative Function
§ 2.5 Leibniz Notation for the Derivative
§ 2.6 The Second Derivative
§ 2.7 Continuity and Differentiability
§ 3.1 Derivatives of Powers and Polynomials
§ 3.2 Derivatives of Exponential Functions
§ 3.3 The Product and Quotient Rules
§ 3.4 The Chain Rule
§ 3.5 Derivatives of Trigonometric Functions
§ 3.6 Applications of the Chain Rule

§ 3.7 Implicit Differentiation
§ 3.8 Parametric Equations
§ 3.9 Linear Approximation and Differentials
§ 3.10 L'Hopital's Rule
§ 4.1 Using First and Second Derivatives
§ 4.2 Special Families of Curves
§ 4.3 Global Maxima and Minima
§ 4.4 Applications to Marginality
§ 4.5 Optimization and Modeling
§ 4.6 Hyperbolic Functions
§ 4.7 The Mean Value Theorem
§ 5.1 How Do we Measure Distance Traveled?
§ 5.2 The Definite Integral
§ 5.3 Interpretations of the Definite Integral
§ 5.4 Theorems About Definite Integrals
§ 6.1 Antiderivatives Graphically and Numerically
§ 6.2 Constructing Antiderivatives Analytically
§ 6.3 Differential Equations
§ 6.4 Second Fundamental Theorem of Calculus
§ 6.5 Motion in One Dimension

MATH 2914 Lecture Notes

MATH 2914
Lecture Notes