Basic Mathematics - Syllabus

Definition, domain, and range of functions. Understanding the concept of functions and their representations.

Understanding the graphical representation of functions, including the vertical line test and piecewise defined functions.

Introduction to common functions including linear, power, polynomial, and rational functions.

Shifting and scaling graphs, sums, differences, products, and quotients of functions, and composite functions.

Using calculators and computers to plot graphs of functions.

Definition, exponential behavior, and exponential growth and decay.

Understanding inverse functions and logarithms.

Understanding the rate of change and tangent to curves.

Overview of the development and evolution of the Linux operating system.

Understanding kernel modules, their types, and their role in extending Linux kernel functionality.

Managing processes in Linux, including process creation, synchronization, and termination.

Linux scheduling algorithms and their role in allocating system resources to processes.

Methods and mechanisms for communication between processes in Linux.

Introduction to distributed database concepts and their advantages.

Techniques for data fragmentation, replication, and allocation in distributed databases.

Methods and approaches for designing distributed databases.

Overview of different types of distributed database systems.

Introduction to finding extreme values of functions, including maximum and minimum values.

The mean value theorem, including Rolle's Theorem and Lagrange Mean Value Theorem, with no proof.

Understanding increasing and decreasing functions using the first derivative test.

Analyzing concavity and sketching curves using differentiation.

Solving indeterminate forms using L'Hopital's Rule.

Applying differentiation to solve optimization problems.

Using Newton's method for finding roots of functions.

Overview of E-commerce and its significance in the digital age.

Understanding the differences between E-business and E-commerce.

Key characteristics and benefits of E-commerce.

Types of E-commerce models and their applications.

Evolution and development of E-commerce over time.

Understanding the components of E-commerce framework including People, Public Policy, Marketing and Advertisement, Support Services, and Business Partnerships.

Overview of different types of E-commerce including B2C, B2B, C2B, C2C, M-Commerce, U-commerce, Social-Ecommerce, and Local E-commerce.

This topic covers the application of definite integrals to find volumes of solids using the method of cylindrical shells. It includes worked out examples to illustrate the concept.

This topic explains how to find volumes of solids using the method of cross-sections and definite integrals. It includes worked out examples to demonstrate the application.

This topic discusses the use of definite integrals to find the length of an arc of a curve. It includes several worked out examples to illustrate the concept.

This topic covers the application of definite integrals to find the area of surfaces of revolution. It includes worked out examples to demonstrate the concept.

Understanding the concept of a file and its importance in C programming.

Opening, closing, naming, and basic operations on files in C.

Reading data from and writing data to a file in C, including functions such as fgetc(), fputc(), fprintf(), and fscanf().

Using functions ftell(), fseek(), and rewind() to access and manipulate file pointers in C.

This topic covers the different types of statistical hypotheses, including null and alternative hypotheses, and their roles in hypothesis testing.

This topic explains the concept of power of the test, p-value, and its use in decision making during hypothesis testing.

This topic outlines the steps involved in testing a hypothesis, from formulating the hypothesis to making a decision based on the test results.

An overview of computers and their significance in today's world. This topic sets the stage for understanding the basics of computers.

Understanding the difference between digital and analog computers, their characteristics, and applications.

Exploring the key characteristics of computers, including input, processing, storage, and output.

A brief history of computers, from their inception to the present day, highlighting key milestones and developments.

Introduction to functions that depend on multiple variables, including definitions and examples.

Understanding limits and continuity of functions in higher dimensions, including examples and exercises.

Definition and calculation of partial derivatives, including worked-out examples and exercises.

Application of the chain rule to partial derivatives, including worked-out examples.

Definition and calculation of directional derivatives, including worked-out examples.

Introduction to tangent planes and differentials, including worked-out examples.

Finding extreme values and saddle points of functions using partial derivatives, including worked-out examples and exercises.