Unit: Analytical Application of Differentiation Chapter: Optimization & Implicit Relations Reference: – Lagrange Multipliers, Optimization problems involving functions, Global maximum & minimum points, Critical points & Significance, Implicit differentiation with Inverse functions, Normal lines to implicit curves, Higher Dimensions, Interpreting & Analysing equations. After studying this chapter, you should be able to: Introduction, General […]
Unit: Integration & Accumulation of Change Chapter: Accumulation Change over an Interval Reference: – Riemann sums, Definite integrals, Fundamental theorem, Antiderivatives, Area under a curve, Accumulation functions, Average value of functions, Mean value theorem for Integrals, Properties & Estimation, Trapezoidal rule, Simpson's Rule, Application & Motion problems. After studying this chapter, you should be […]
Unit: Integration & Accumulation of Change Chapter: Approximation Integrals using Riemann Sums Reference: – Riemann sums, Partition of an interval, Left & Right Riemann sum, Midpoint, Lower & Upper Riemann sums, Rectangular & Trapezoidal approximations, Composite Riemann sums, Width & Subintervals, Error Estimation. After studying this chapter, you should be able to: Introduction to […]
Unit: Integration & Accumulation of Change Chapter: Fundamental Theorem of Definite Integral Reference: – Antiderivatives, Indefinite integrals, Definite integrals, Fundamental theorem of Calculus, Part 1 & Part 2 of FTC, Evaluation using Antiderivatives, Reverse power rule, Initial value problem, Area under the curve, Mean value theorem & Properties, Applications. After studying this chapter, you […]
Unit: Integration & Accumulation of Change Chapter: Antiderivatives & Indefinite Integrals Reference: – Antiderivatives, Indefinite integrals, Power rule, Constant Multiple rules, Sum & Difference rule, Integration by Substitution & Parts, Trigonometric integrals, Partial fraction decomposition, Rational function Integrals, Improper integrals, Application of Antiderivatives & Indefinite integrals. After studying this chapter, you should be able […]
Unit: Integration & Accumulation of Change Chapter: Properties of Integrals & Techniques Reference: – Riemann sums, Definite integrals, Fundamental theorem, Antiderivatives, Area under a curve, Accumulation functions, Average value of functions, Mean value theorem for Integrals, Properties & Estimation, Trapezoidal rule, Simpson's Rule, Application & Motion problems. After studying this chapter, you should be able […]
Unit: Differential Equation Chapter: Separable Differential Equation Reference: – 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: Separation of Variables & […]
Unit: Differential Equation Chapter: Slope Field & Solution Curves 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: The direction of Solution & Curve. Equilibrium […]
Unit: Differential Equation Chapter: General & Particular Solution 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: First Order & Second Order Differential Equation. General solution & Particular solution. Boundary […]
Unit: Differential Equation Chapter: Exponential Growth & Decay 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: Simple Growth & Decay Model. […]