Calculus 1
The following learning targets represent the major concepts studied and assessed in this course.
Unit P
Precalculus Review
- P.1 Graphs and Models
- P.2 Linear Models and Rates of Change
- P.3 Functions and Their Graphs
- P.4 Fitting Models to Data
Unit 1
Limits and Continuity
- Introduction to calculus and limits
- Finding limits graphically and algebraically
- Limits and continuity
- Infinite limits
- Special limits - squeeze theorem and intermediate value theorem
Unit 2
Differentiation: Definition and Properties
- Definition of the derivative
- Power rule of the derivative
- Product and quotient rule of the derivative
- Chain rule of the derivative
- Implicit differentiation
Unit 3
Related Rates and Other Applications of Derivatives
- Related Rates
Unit 4
Differentiation: Transcendental and Inverse Functions
- Derivative of exponential and logarithmic functions
- Derivatives of inverse functions
- Derivatives of inverse trigonometric functions
Unit 5
Analytical Applications of Derivatives
- Introduction to graphs of derivatives
- Extreme values and critical numbers
- First derivative test
- Second derivative test
- Mean value theorem
- L’Hopital’s rule
- Optimization
Unit 6
Integration and Area Under a Curve
- Basic integration - power rule
- U-Substitution of integration
- Area under the curve
- Area under the curve with summation and definite integral
- Fundamental theorem of calculus
- Applications of integration
Unit 7
- Area between two curves
- Disk and washer method for a solid of revolution
- Slope fields