Calculus serves as the foundation of advanced subjects in all areas of mathematics. This is the first course of Calculus. The objective of this course is to introduce students to the fundamental concepts of limit, continuity, differential, and integral calculus of functions of one variable.
|Inquiry Based Session-1 lesson||1||25$|
|Regular Package/ 4 lesson||4||100$|
|Standard Package/8 Lesson||8||180$|
|Fast Track/16 Lesson||16||320$|
Equations and inequalities: Solving linear and quadratic equations, linear inequalities. Division of polynomials, synthetic division. Roots of a polynomial, rational roots; Viete Relations. Descartes' rule of signs. Solutions of equations with absolute value sign. Solution of linear and non-linear inequalities with absolute value sign.
Functions and graphs: Domain and range of a function. Examples: polynomial, rational, piecewise-defined functions, the absolute value of functions, and evaluation of such functions. Operations with functions: sum, product, quotient, and composition.
Graphs of functions: linear, quadratic, piecewise-defined functions. Lines and systems of equations: Equation of a straight line, slope, and intercept of a line, parallel and perpendicular lines. Systems of linear equations, solution of a system of linear equations. Nonlinear systems: at least one quadratic equation.
Limits and continuity: Functions, limit of a function. Graphical approach. Properties of limits. Theorems of limits. Limits of polynomials, rational and transcendental functions. Limits at infinity, infinite limits, one-sided limits. Continuity.
Derivatives: Definition, techniques of differentiation. Derivatives of polynomials and rational, exponential, logarithmic, and trigonometric functions. The chain rule. Implicit differentiation. Rates of change in natural and social sciences. Related rates. Linear approximations and differentials. Higher derivatives, Leibnitz's theorem.
Applications of derivatives: Increasing and decreasing functions. Relative extrema and optimization. First derivative test for relative extrema. Convexity and point of inflection. The second derivative test for extrema. Curve sketching. Mean value theorems. Indeterminate forms and L'Hopitals rule. Inverse functions and their derivatives.
Integration: Anti derivatives and integrals. Riemann sums and the definite integral. Properties of Integral. The
fundamental theorem of calculus. The substitution rule.
Hi, I am Dr. Muhammad Usman graduated from Peking University in the field of applied and computational mathematics with distinguished student. I also completed my postdoc in field of computational mathematics. I have numerous research articles published in well-reputed international journals. Therefore, I have rich experience in research and supervise project students. As for as my teaching career is concerned, I have 14 years’ experience in teaching. I have taught various courses at A-level, O-level, graduate and postgraduate level. In the recent past years, I involve extensively in teaching online at A-level and O-level. Positive feedback of my past students always encourage me to deliver more in the better way. I look forward to working together with you as partners in your child’s educational growth and development!!