sub content

Calculus I : Pokhara University Notes and Exercise

Get Calculus I Calculus i notes comprehensive notes, detailed Q&As, and past question papers solutions and video tutorials.

Calculus note all exercise solution

sn	Notes
1	Calculus All Exercise Solution (Find From Below Notes Section )

Syllabus

Unit I: Limit Continuity and Derivatives (5 hrs)
1.1 Introduction
1.2 Limit, continuity and differentiability
1.3 Higher order derivatives by Leibnitz method.

Unit II: Applications of Derivatives (8 hrs)
2.1 Mean value theorems: Rolle’s theorem, Lagrange’s
Theorem (Geometrical interpretation and verification) and
applications
2.2 Higher order mean value theorem: Taylor’s Series,
Maclaurin’s Series expansion of function.
2.3 Asymptotes to Cartesian curves up to four degrees.
2.4 Curve tracing in Cartesian form and parametric form
2.5 Curvature

Unit III: Integral Calculus (6 hrs)
3.1 Introduction
3.2 Review on Indefinite Integral and fundamental theorem of integral calculus.
3.3 Definite integral and its properties
3.4 Improper Integrals; comparison test.
3.5 Reduction formula, Beta Gamma function

Unit IV: Application of Integral (6 hrs)
4.1 Application of integrals for finding area beneath a curve
and between two curves and arc length
4.2 Surface and volume of solid of revolution in the plane for
Cartesian and parametric curves.

Unit V: Partial Differentiation (3 hrs)
5.1 Introduction
5.2 Partial Derivatives
5.3 Homogeneous function and Euler’s theorem for the
function of two and three variables
5.4 Total Derivatives and Differentiation of Implicit
functions.

Unit VI: Application of Partial Differentiation (4 hrs)
6.1 Extrema of functions of two and three variables.
6.2 Lagrange’s method of undetermined Multipliers (up to 2
multipliers)

Unit VII: First Order Ordinary Differential Equations
(6 hrs)
7.1 Review of separable, homogeneous and exact differential
equation with engineering applications
7.2 Linear, Bernoulli equation and Riccati’s equation with
engineering application.
7.3 Mathematical modeling of engineering problems using
first order equation.

Unit VIII: Second Order Ordinary Differential Equations
(7 hrs)
8.1 Second order Homogeneous ODE with constant and
variable coefficients, Euler-Cauchy equation.
8.2 Existence and uniqueness of solutions, Wronskian and
general solutions for solving ODE.
8.3 Non-homogeneous second order ODE and Solution by
undetermined coefficients and variation of parameters and
engineering application