Unit: Parametric Equations, Polar Coordinates & Vector-Valued Function Chapter: Position of Particles Moving in plane Reference: – Position vectors, Velocity vectors, Acceleration vectors, Scalar & Vector functions, Tangent vector, Tangent lines, Normal vector, Normal lines, Curvature & Arc length of a curve, Projectile Motion & Relative motion, Polar equations, Application of Vector calculus After studying […]
Unit: Parametric Equations, Polar Coordinates & Vector-valued function Chapter: Accumulation of 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 […]
Unit: Parametric Equations, Polar Coordinates & Vector-Valued Function Chapter: Derivatives of Parametric & Vector-valued Functions Reference: – Parametric equations, Parametric curves, Tangent lines, Normal lines, Arc length, Curvature, Acceleration, Tangent Vectors, Normal Vectors, Binormal vectors, Unit Tangent, Planar curves, Polar coordinates, Applications & Properties After studying this chapter, you should be able to: Introduction […]
Unit: Infinite Sequence & Series Chapter: Taylor Series, Maclaurin Series Reference: – Divergence test, Geometric series, Integral test, Comparison test, Limit comparison test, Alternating series test, Absolute convergence, Conditional Convergence, Ratio test, Root test, Taylor series, Radius of convergence, Interval of convergence. After studying this chapter, you should be able to: Introduction to Taylor […]
Unit: Application of Integrations Chapter: Modeling Particle Motion & Accumulation Problems Reference: – Motion Particle, 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: Purpose of topic […]
Unit: Application of Integrations Chapter: Value of Function by Definite Integral 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: Identifying the Function & […]
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. […]
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: 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: 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 & […]