MATHEMATICS 2 : solved Exercices : for first year university students in matter sciences and related disciplines.
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Date
2025
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Publisher
Faculty of Sciences
Abstract
The more you practice mathematics, the more proficient you become
just like with any other skill. Mastering a mathematics course, how-
ever, goes beyond the rote memorization of rules, laws, and theorems. It
prioritizes a deep understanding of the underlying concepts through consis-
tent problem-solving, the application of various techniques, and the use of
logical reasoning.
This handout presents a collection of solved mathematical exercises in-
tended for first-year undergraduate students in Matter Sciences (SM). Its
primary aim is to provide students with a solid foundation while fostering
rigorous scientific reasoning, thereby helping them master key concepts and
better understand physical and chemical laws, phenomena, and models
especially those that are often challenging to grasp.
The document addresses key topics in analysis and linear algebra as out-
lined in the Mathematics 2 syllabus. It is structured into four chapters:
Chapters 1, 3, and 4 focus on concepts from analysis, while Chapter 2 con-
centrates on topics from linear algebra. Each chapter begins with a brief
overview of the main notions, followed by a set of fully solved exercises designed to reinforce learning through guided practice and problem-solving.
Chapter 1 deals with solving first- and second-order linear ordinary dif-
ferential equations using different methods such as the integrating factor
method and variation of parameters.
Chapter 2 focuses on linear algebra, emphasizing matrices, determinants,
diagonalization, and systems of linear equations.
Chapter 3 includes exercises with detailed solutions on Taylor series ex-
pansions.
Chapter 4 presents problems involving differential operators, as well as
limits and partial derivatives of functions of two variables.
The methodology employed here aims to encourage active learning, strengthen
mathematical rigor, and bridge theoretical understanding with practical ap-
plications.
The detailed table of contents at the beginning of the document enables
students to navigate the material efficiently and locate specific topics as
needed.