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: 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: 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: 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: 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: Analytical Application of Differentiation Chapter: Graph of Functions & Derivatives Reference: – Cartesian Coordinate system, Interpretation of a function, Domain & Range, Graphical representation, Symmetry of functions, Transformations of functions, Even and odd functions, Global extrema on the graph, Graphical Interpretation of derivatives. After studying this chapter, you should be able to: Continuity, […]
Unit: Analytical Application of Differentiation Chapter: First & Second Order Test Reference: – Rolle’s Theorem, Intermediate value theorem, Extreme values, Critical points, Local extrema, Absolute extrema, closed intervals, First & Second derivative test, Concavity, Inflection points, Approximate values, Mean value theorem for integrals, Average value functions. After studying this chapter, you should be able to: […]
Unit: Analytical Application of Differentiation Chapter: Derivatives & Properties of a Function Reference: – Differentiability & Continuity, Increasing & Decreasing functions, Curve sketching, Analysis of a function, Optimization problems, First & Second Derivative test, Related rates, Local extrema, Implicit differentiation & Applications. After studying this chapter, you should be able to: Basic Concept of […]
Unit: Analytical Application of Differentiation Chapter: Mean & Extreme Value Theorem Reference: – Rolle’s Theorem, Intermediate value theorem, Extreme values, Critical points, Local extrema, Absolute extrema, closed intervals, First & Second derivative test, Concavity, Inflection points, Approximate values, Mean value theorem for integrals, Average value functions. After studying this chapter, you should be able […]
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 […]