MPI Calculus 1 and 2
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
Transcendental and Inverse Derivatives
- Transcendental derivatives
- Derivatives of inverse functions
- Derivatives of inverse trig functions
- L’Hopital’s rule
Unit 4
Applications of the Derivative - Curve Sketching
- Position, velocity, and acceleration applications of the derivative
- Extreme values and crucial numbers
- First derivative test for increasing/decreasing/minimum/maximum
- Second derivative test for concavity and points of inflection
Unit 5
Analytical Applications of Derivatives
- Mean value theorem
- L’Hopital’s rule
- Related rates
- Optimization
Unit 6
Integration and Accumulation of Change
- Indefinite integrals
- U-Substitution of integration
- Area under the curve and definite integrals
- Area under the curve with summation and definite integral
- Accumulation function
- Summation formulas and properties
- Riemann sums and area with summation
- Fundamental theorem of calculus
Unit 7
Transcendental Integration
- Natural log integration
- Exponential functions integration
- Inverse trigonometric integrals
Unit 8
Applications of Integration
- Area between curves
- Disk and washer method for a solid of revolution
- Shell method for solids of revolution
- Arc length and surface area
- Work
- Moments and centers of mass
- Fluid force and pressure
Unit 9
Complex Integration
- Basic integration rules
- Integration by parts
- Trigonometric integration
- Trigonometric substitution
- Partial fractions
- Improper integrals
Unit 10
Sequences and Series
- Sequences and limits
- Series and convergence
- P-series and integral test
- Comparison test
- Alternating series test
- Ratio and root test
Unit 11
Parametric and Polar Equations
- Conics and calculus
- Parametric equations
- Parametric equations and calculus
- Polar coordinates and graphs
- Polar graphs