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: 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: Contextual Application of Differentiation Chapter: L’Hospital’s rule Reference: – Statement & Condition, Rule for limits, Rule for Exponential & logarithmic functions, Hyperbolic functions, Limits at Infinity, Indeterminate form involving power, Factorial & rational functions, Limits involving sequences, Applications & Mathematical analysis. After studying this chapter, you should be able to: Indeterminate forms-Statement & Condition. […]
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 […]