Math Byte Course Topics:
Course Topics are organized as six modules with five granular topics covered under each module. Click through below to see all modules/topics for this course.
01 - Limits/Derivatives
- Riemann Sums
- Integration by Substitution, Trigonometric Substitutions
- Integration by Parts
- Partial Fraction Decomposition
- Improper Integrals and Definite Integral Manipulations
02 - Evaluating Integrals
- Riemann Sums
- Integration by Substitution, Trigonometric Substitutions
- Integration by Parts
- Partial Fraction Decomposition
- Improper Integrals and Definite Integral Manipulations
03 - Applications of Integration
- Average Value of a function, Mean Value Theorem, Intermediate Value Theorem
- Areas of Bounded Regions
- Solids of Revolution, Solids with Cross Sections
- Arc Length
- Moment of Inertia
04 - Differential Equations
- Introducing Differential Equations
- Euler's Method of Approximations and Slope Fields
- Solving Separable Differential Equations
- Logistic and Exponential Functions
- Modeling / Population Growth
05 - Parametric and Polar
- Derivatives of Parametric and Vector Valued Functions
- Accumulation of Change with Definite Integrals, Integration to find position of a particle
- Speed, Velocity Vectors, and Acceleration Vectors of a particle
- Derivatives of Polar Functions, Introduction to finding areas bounded by polar functions
- Areas of regions bounded by polar curves
06 - Sequences and Series
- Definition of Convergence, Absolute Convergence, Conditional Convergence with Limits
- Basis types of series (Geometric, Harmonic, p-series), Convergence and Divergence tests
- Alternating Series Error Bound, Approximating convergent series
- Introduction to Taylor and Maclaurin Series, Interval and radius of convergence
- Taylor's Theorem, Lagrange Error Bound, Calculating and Manipulating power series with derivatives and integrals
