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Calculus
Calculus is defined as the mathematical study of continuous change, motion, and the behavior of functions using the concept of limits.
- Chapter 1Lesson ready
Limits and Continuity
- Evaluating limits algebraically, graphically, and numerically.
- Asymptotes and the Intermediate Value Theorem.
- Chapter 2Outline
Differentiation
- The formal limit definition of a derivative.
- Power, product, quotient, and chain rules.
- Implicit differentiation.
- Chapter 3Outline
Applications of Differentiation
- Position, velocity, and acceleration kinematics.
- Optimization and related rates.
- Curve sketching (concavity, local extrema, points of inflection).
- Chapter 4Outline
Integration and Accumulation of Change
- Riemann sums and the Fundamental Theorem of Calculus.
- Techniques of integration (u-substitution, integration by parts, partial fractions).
- Improper integrals.
- Chapter 5Outline
Applications of Integration
- Area between curves.
- Volume of solids with known cross-sections and solids of revolution.
- Arc length.
- Chapter 6Outline
Differential Equations
- Slope fields and Euler's Method.
- Separable differential equations.
- Logistic growth models.
- Chapter 7Outline
Parametric, Polar, and Vector-Valued Functions
- Derivatives and integrals of parametric and polar curves.
- Vector kinematics in 2D space.
- Chapter 8Outline
Infinite Sequences and Series
- Convergence tests (Ratio, Root, Integral, Comparison, Alternating).
- Maclaurin and Taylor Series approximations.
- Radius and interval of convergence.
- Chapter 9OptionalOutline
Vectors and Multivariable Calculus
- Vectors in space: dot products, cross products, and projections.
- Functions of several variables, partial derivatives, and the gradient.
- Double integrals and volume over a region.
9 of 9 chapters