Unit: Contextual Application of Differentiation Chapter: Rates, Linearity & Approximation Reference: – Average rate of change, Slope of a line, Tangent line, Derivatives, Linear approximation, Linear functions & Graphs, Piecewise linear functions, Indeterminate form, Continuity of a function, Taylor series, Maclaurin series, Linear regression. After studying this chapter, you should be able to: Introduction, […]
Unit: Contextual Application of Differentiation Chapter: Generalizing Motion to rate of Change Reference: – Polar Coordinates, 3- Dimensional motion, Circular motion, Curvature, Projectile Motion, Chain rule, Tangent & Normal Vectors, Fundamental Theorem, Notations & its applications. After studying this chapter, you should be able to: Average & Instantaneous rate of change. Tangent line, Derivatives […]
Unit: Contextual Application of Differentiation Chapter: Differentiation with Motion Reference: – Position & Acceleration functions, Instantaneous velocity Functions, Tangent lines, Rate of change, Derivative of velocity functions, Maximum & Minimum value functions, Particle motion in a straight line, Projectile motion, motion along curves, Applications & Properties. After studying this chapter, you should be able to: […]
Unit: Contextual Application of Differentiation Chapter: Differentiation with Rate of Change Reference: – Differentiation, its types, Implicit differentiation, Related rates, Local extrema, Critical points, Increasing & Decreasing functions, Concavity, Points of inflection, Linear Approximation, Mean value theorem, Newton's method, Antiderivatives, Indefinite integrals, Applications. After studying this chapter, you should be able to: Introduction, Notation […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: High-Order Derivative Functions Reference: – First & Second derivative, Higher order derivative, Notations, Power rule, Product rule, Quotient rule, Chain rule, Differentiation of higher order, Exponential function, Logarithmic & Polynomial Functions, Concavity, Inflection point & Applications. After studying this chapter, you should be able to: Introduction to 1st […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: General Inverse Functions Reference: -Inverse functions, One to-one functions, Invertibility, Inverse algebraically, Graphing the inverse functions, Equations & Graphs, Composition of inverse functions, Domain & Range of Inverse functions, Derivatives of Inverse functions, Applications & Properties. After studying this chapter, you should be able to: Introduction & Verification […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: Implicit Differentiation Reference: – Implicit Functions, Implicit equations, Derivatives of Implicit relations, Chain rules, Slope of tangent lines, Equation of tangent line, Implicit differentiation, Higher order derivatives, vertical & Horizontal Tangent lines, Curve sketching, Optimization, Trigonometric Functions. After studying this chapter, you should be able to: Differentiation Rule […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: Chain Rule for Composite Functions Reference: – Composite Functions, Differentiation of composite functions, Chain rule, Power functions, Exponential functions, Logarithmic functions, Hyperbolic functions, Implicit, Multiple compositions, Parametric equations, Higher Dimensions, Partial Derivatives. After studying this chapter, you should be able to: Composite functions & its Differentiation. Nested function […]
Unit: Differentiation-Fundamental Properties Chapter: Elementary Functions Reference: – Elementary Functions, Polynomial Functions, Exponential functions, Logarithmic functions, Power rules, Trigonometric functions, Composite functions, Chain rules, Quotient rules, Inverse functions, Rational functions, Domain & Range, Absolute value functions. After studying this chapter, you should be able to: Introduction & Basic rules. Types & Application of Elementary Function. […]
Unit: Differentiation-Fundamental Properties Chapter: Continuity & Differentiability Reference: – Continuous, Discontinuous, Point of Discontinuity, Removable Discontinuity, jump discontinuity, Tangent line, Differentiation, Derivatives, Cusp, Critical point, Piecewise function, Continuity implication, Types of continuity & Differentiability, Mixed properties, Rules & Formation. After studying this chapter, you should be able to: Fundamental Properties of Continuous Function. Continuities […]