Single Variable Calculus

01 Functions
1.1 Functions
1.2 Exponents1.3 Logarithmic Functions
1.4 Trigonometric Equations
Multiple Choice

02 Limits and Continuity
2.1 Limit Existence
2.2 Squeezing Theorem (Sandwich Theorem)
2.3 Limit of Trigonometric Function
2.4 Limit of Exponential and Logarithmic Functions
2.5 Limits Involving Infinity
2.6 Continuity
2.7 Average Rate of Change and Instantaneous Rate of Change
2.8 Intermediate Value Theorem (I.V.T.)
Multiple Choice

03 Derivatives
3.1 Definition of Derivative
3.2 Differentiability
3.3 Power Rule
3.4 Product Rule
3.5 Quotient Rule
3.6 Chain Rule
3.7 Implicit Differentiation
3.8 Higher Order Derivatives
3.9 Derivatives of Trigonometric Functions
3.10 Derivatives of Exponential Functions
3.11 Derivatives of Logarithmic Functions
3.12 Inverse Trigonometric Functions
3.13 Derivatives of Inverse Trigonometric Functions
3.14 Derivatives of Inverse Functions
Multiple Choice

04 Application of Derivatives
4.1 Critical Points
4.2 Extrema: Maximum & Minimum value
4.3 Concavity
4.4 Curve Sketching
4.5 Relation of f'(x), f''(x) to the Graph of f(x)
4.6 Motion Along a Line (1-Dimension)
4.7 Motion Along a Curve: Velocity and Acceleration Vectors
4.8 Modeling and Optimization
4.9 Related Rates
4.10 Mean Value Theorem (M.V.T)
4.11 Local Linear Approximation
4.12 Newton's Method
4.13 Approximating Derivatives Numerically
4.14 Indeterminate Forms and L'Hospital's Rule
Multiple Choice

05 Integration
5.1 Indefinite Integrals
5.2 Integration by Substitution
5.3 Integration by Parts
5.4 Rectangular Approximation Method (RAM)
5.5 Trapezoidal Approximation
5.6 Definition of Area as a Limit
5.7 Definite Integrals
5.8 Fundamental Theorem of Calculus, Part I
5.9 Fundamental Theorem of Calculus, Part II
5.10 Area between a curve and the x-axis
5.11 Substitution for Definite Integrals
5.12 Integration by Parts for Definite Integrals
5.13 Even and Odd Functions
5.14 Integration by Partial Fraction
Multiple Choice

06 Applications of Definite Integrals
6.1 Average Value of a Function
6.2 Area Between Curves
6.3 Volume of Solids with Known Cross Sections
6.4 Volume of Solids of Revolution:
Disk, Washers and Cylindrical Shells
6.5 Definite Integral of a Rate is Net Change
6.6 Motion Along a Straight Line (1-Dimension)
6.7 Motion Along a Plane Curve
6.8 Arc Length
6.9 Improper Integrals
Multiple Choice

07 Differential Equations
7.1 Slope Fields (Direction Fields)
7.2 First Order Separable Differential Equations
7.3 Exponential Growth and Decay
7.4 Euler's Method
7.5 Logistic Growth
Multiple Choice

Solution
Index

민만식 Mansik Min
Department of AI and Big Data, Suwon University
Ph.D. in Statistics, Korea University