AKTU Mathematics – Differential Calculus and Linear Algebra (AAS103A/AAS103B/AAS103C/G) Notes & Study Material PDF – B.Tech 1st Year Sem 1

📘 AKTU B.Tech 1st Year Differential Calculus & Linear Algebra – Complete Study Notes

Prepare smarter for your AKTU B.Tech First Year Mathematics examination with this comprehensive 146-page study resource covering:

Differential Calculus and Linear Algebra

Course Codes: AAS103A / AAS103B / AAS103C / AAS103G
Programme: B.Tech. First Year
Academic Session: 2026–27

This unique EduQuest resource combines the overlapping content of the four stream-specific AKTU syllabi into a single, unified study book, allowing students from Civil, Mechanical, Electrical/Electronics and Chemical Engineering streams to study from one comprehensive resource.

✨ What You'll Get

✔ Complete syllabus-oriented study material
✔ Easy-to-understand mathematical explanations
✔ Key formulas and definitions highlighted
✔ Step-by-step solved examples
✔ Mathematical diagrams and geometric illustrations
✔ IMPORTANT & MOST IMPORTANT topic tags
✔ Unit-wise question banks
✔ Short-answer questions
✔ Long-answer / descriptive questions
✔ Examination-oriented questions
✔ AKTU-pattern Sample Model Question Papers
✔ Consolidated formula sheet
✔ Quick revision checklist
✔ Glossary of important mathematical terms

Every unit concludes with a structured question bank divided into Short Answer, Long Answer/Descriptive and Important Examination-Oriented Questions.

📚 Complete Unit CoverageUNIT I – Matrix Algebra

Topics include:

• Introduction to Matrices
• Elementary Transformations
• Rank of a Matrix
• Echelon Form
• Solution of Linear Systems
• Gauss Elimination Method
• Gauss–Seidel Method
• Eigenvalues and Eigenvectors
• Diagonalization
• Engineering Applications of Matrix Algebra

The unit also connects matrix techniques with engineering applications such as structural analysis, finite element analysis, transportation networks, machine dynamics, electrical networks, CAD and machine learning.

UNIT II – Differential Calculus

Covers:

• Limits
• Continuity
• Differentiability of Functions of Two Variables
• Partial Derivatives
• Composite Functions
• Total Derivatives
• Euler's Theorem
• Homogeneous Functions
• Taylor's Expansion
• Maclaurin's Expansion
• Jacobians
• Maxima and Minima of Functions of Two Variables

These topics are organized as a complete unit with a dedicated question bank for examination practice.

UNIT III – Multiple Integrals

Includes:

• Double Integrals
• Triple Integrals
• Change of Order of Integration
• Change of Variables
• Polar Coordinates
• Beta Functions
• Gamma Functions
• Dirichlet's Integral
• Area of Irregular Surfaces
• Volume of Solids
• Engineering Applications
• Fluid Mechanics and Hydraulics

The notes explain the concepts with worked examples, including changing the order of integration and applications to engineering problems.

UNIT IV – Vector Spaces

For AAS103A / AAS103B / AAS103C, the resource covers:

• Vector Spaces
• Subspaces
• Spanning Sets
• Linear Independence
• Basis and Dimension
• Linear Transformations
• Range and Null Space
• Rank-Nullity Theorem
• Matrix of a Linear Transformation
• Engineering Applications of Vector Spaces

The book includes key definitions and formulas such as the subspace test, linear independence, basis, dimension and rank-nullity theorem.

UNIT V – Ordinary Differential Equations

For AAS103G – Chemical Engineering, this unit covers:

• Linear Differential Equations of nth Order
• Constant-Coefficient Differential Equations
• Cauchy–Euler Equations
• Variation of Parameters
• Differential Equations with Variable Coefficients
• Change of Independent Variable
• Normal Form
• Engineering Applications
• Chemical Reaction Kinetics
• Reactor Design
• Mass Transfer

This unit is specific to the AAS103G syllabus.

UNIT VI – Vector Calculus

Covers:

• Scalar Point Functions
• Vector Point Functions
• Gradient
• Directional Derivatives
• Divergence
• Curl
• Solenoidal Vector Fields
• Irrotational Vector Fields
• Line Integrals
• Stokes' Theorem
• Gauss Divergence Theorem
• Engineering Applications

Vector Calculus is common across all four source course codes.

🎯 Special Advantage: Combined AKTU Course Codes

One of the biggest advantages of this resource is its combined-syllabus approach.

It brings together:

Units I, II, III and VI are common across all four course codes.

Students should, however, follow the units applicable to their own course code and confirm the exact examination requirement with their institution/instructor.

🧮 Step-by-Step Problem Solving

Mathematics requires more than formulas — students need to understand how to apply them.

The notes therefore present solved examples with complete, step-by-step working, rather than simply giving final answers. Key formulas and definitions are boxed for quick revision, while diagrams and geometric illustrations are placed alongside the relevant concepts.

⭐ IMPORTANT & MOST IMPORTANT Topics

The notes use priority tags to make revision more efficient.

★ MOST IMPORTANT

Used for topics that are high-weightage, frequently examined or foundational to later concepts.

★ IMPORTANT

Used for topics regularly asked in short-answer questions or topics that provide essential background.

This allows students to prioritize their preparation when examination time is limited.

📝 AKTU Examination Practice

The book includes two Sample Model Question Papers based on the standard AKTU end-semester examination pattern.

For AAS103A/B/C, the sample paper follows a 3-hour, 70-mark examination structure.

The resource also provides examination-oriented questions throughout the individual unit question banks.

📖 Quick Revision Support

The final portion of the book includes:

• Glossary of Key Terms
• Useful Standard Values
• Consolidated Formula Master Sheet
• Unit Applicability by Course Code
• Quick Revision Checklist

The Formula Master Sheet is specifically designed as a rapid last-minute revision reference.

👨‍🎓 Ideal For

This study material is suitable for:

• AKTU B.Tech 1st Year students
• Civil Engineering students
• Mechanical Engineering students
• Electrical & Electronics Engineering students
• Chemical Engineering students
• Students studying AAS103A
• Students studying AAS103B
• Students studying AAS103C
• Students studying AAS103G
• Students preparing for AKTU semester examinations
• Students looking for comprehensive Mathematics study material
• Students who need structured numerical/problem-solving practice