Calculus – I Books – Aarogya K.C.

Comprehensive Guide to Pokhara University Semester 1 Calculus-I Important Books and Study Resources

Starting your journey as a Bachelor of Engineering (BE) student at Pokhara University brings exciting academic challenges, especially when mastering foundational mathematical courses. For BE Civil Engineering students in their …

Calculus I Syllabus, Textbooks & Reference Books

Calculus I is a foundational mathematics course for
Bachelor of Engineering (BE) students under
Pokhara University, Faculty of Science and Technology.
This category contains the official syllabus, recommended textbooks, and reference books designed to help BE students master differential and integral calculus, partial differentiation, and ordinary differential equations.

Course Overview & Details

Course No.: MTH 110
Course Title: Calculus I
Program: BE (Bachelor of Engineering)
Level: Bachelor
Nature: Theory
Full Marks: 100
Pass Marks: 45
Total Lectures: 45 Hrs

Recommended Books & Study Materials

To prepare effectively for exams and gain a strong conceptual understanding, students should refer to standard calculus textbooks and reference books that cover the complete Pokhara University syllabus:

Standard Engineering Mathematics Textbooks: Comprehensive books covering limits, derivatives, integration, and differential equations with solved engineering problems.

Reference Books & Solution Guides: Step-by-step problem-solving books for curve tracing, Lagrange multipliers, Beta-Gamma functions, and ODEs.

Pokhara University Textbook Resources: Prescribed calculus books aligned directly with the MTH 110 syllabus structure.

Complete Syllabus & Course Contents

Unit I: Limit, Continuity and Derivatives (5 Hrs) –
Limits, continuity, differentiability, and higher-order derivatives using Leibnitz’s method.

Unit II: Applications of Derivatives (8 Hrs) –
Mean value theorems including Rolle’s theorem and Lagrange’s theorem, Taylor and Maclaurin series, asymptotes, curve tracing, and curvature.

Unit III: Integral Calculus (6 Hrs) –
Indefinite and definite integrals, fundamental theorem of integral calculus, properties of definite integrals, improper integrals, comparison tests, reduction formulae, and Beta-Gamma functions.

Unit IV: Applications of Integral Calculus (6 Hrs) –
Finding areas, arc lengths, surface areas, and volumes of solids of revolution using Cartesian and parametric curves.

Unit V: Partial Differentiation (3 Hrs) –
Partial derivatives, homogeneous functions, Euler’s theorem, total derivatives, and differentiation of implicit functions.

Unit VI: Applications of Partial Differentiation (4 Hrs) –
Extrema of functions of two and three variables and Lagrange’s method of undetermined multipliers.

Unit VII: First-Order Ordinary Differential Equations (6 Hrs) –
Separable, homogeneous, exact, linear, Bernoulli, and Riccati equations, along with engineering applications and mathematical modeling.

Unit VIII: Second-Order Ordinary Differential Equations (7 Hrs) –
Homogeneous and non-homogeneous second-order ODEs, constant and variable coefficients, Euler-Cauchy equations, existence and uniqueness, Wronskian, undetermined coefficients, variation of parameters, and engineering applications.

Major Topics Covered in Books

Limits & Continuity •
Differentiation •
Mean Value Theorems •
Taylor & Maclaurin Series •
Curve Tracing •
Curvature •
Integral Calculus •
Beta & Gamma Functions •
Area & Arc Length •
Surface & Volume •
Partial Differentiation •
Extrema •
Lagrange Multipliers •
First-Order ODEs •
Second-Order ODEs •
Engineering Applications

Course Focus & Learning Outcomes

The recommended books and syllabus emphasize the practical use of calculus in engineering analysis, mathematical modeling, optimization, geometry, and differential equation problems. Studying these textbooks provides the mathematical foundation required for advanced engineering subjects.