Applied Maths Solution Class 11 – ML Aggarwal

Class 11 ML Aggarwal Book.

INTRODUCTION

Applied Maths is a branch of mathematics that deals with mathematical methods and techniques that are applied to solve real-world problems in various fields. Mathematics is useful not only to engineering stream students, but it has wide use in higher studies in the fields of economics, commerce, social science, and even in liberal arts. Unlike pure mathematics, which focuses on abstract concepts and theories, applied mathematics aims to use mathematical tools to understand and solve practical problems that arise in other disciplines.

Mathematics is a beautiful and interesting branch of study and has widespread use in many areas of life. However, many students have an unnecessary fear of mathematics. Our efforts are to provide a logical sequence to develop and strengthen the concepts.

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HOW APPLIED MATHS IS HELPFUL FOR COMMERCE STUDENTS:

Applied Maths can be incredibly helpful for commerce students in several ways:

1. Finance Analysis and Modeling: Commerce students often deal with financial data, such as budgets, investments, and financial statements. Applied mathematics provides tools for analyzing this data, developing models to predict future trends, and making informed decisions about investments, pricing strategies, risk management, and more.
2. Optimization: Applied mathematics offers techniques for optimizing various aspects of business operations, such as production schedules, inventory management, resource allocation, and supply chain logistics. Commerce students can use optimization methods to maximize profits, minimize costs, and improve overall efficiency.
3. Statistics and Data Analysis: Understanding statistical methods is essential for interpreting data and making informed decisions in commerce. Applied mathematics provides a framework for statistical analysis, hypothesis testing, regression analysis, and other techniques that are valuable for analyzing market trends, consumer behavior, and business performance.
4. Risk Management: Commerce students need to understand and manage risks associated with financial investments, business operations, and market fluctuations. Applied Maths provides tools for quantifying and managing risks, such as probabilistic models, Monte Carlo simulations, and option pricing models.
5. Decision Support System: Applied Maths plays a crucial role in developing decision support systems and business intelligence tools that help businesses make data-driven decisions. Commerce students can learn how to use mathematical models and algorithms to analyze complex data sets, identify patterns, and generate insights that support strategic planning and decision-making.

THE MAIN DIFFERENCES BETWEEN APPLIED MATHEMATICS AND CORE MATHEMATICS LIES IN THEIR FOCUS, SCOPE, AND APPLICATION:

1. FOCUS:

• Core Mathematics: Core mathematics, also known as pure mathematics, focuses on studying abstract concepts and theoretical principles within mathematics itself. It deals with fundamental mathematical structures, such as algebra, calculus, geometry, number theory, and logic, without necessarily considering their direct applications to real-world problems.
• Applied Mathematics: Applied mathematics, on the other hand, emphasizes the use of mathematical techniques and methods to solve practical problems in various fields, including science, engineering, economics, computer science, and more. It involves the application of mathematical concepts to analyze real-world phenomena, develop models, make predictions, and solve specific problems.

1. SCOPE:

• Core Mathematics: Core mathematics explores the underlying principles and theories of mathematics, often delving into abstract concepts and proving theorems. Topics may include mathematical structures, formal systems, abstract algebra, real analysis, complex analysis, and more.
• Applied Mathematics: Applied Maths encompasses a wide range of topics and techniques, including mathematical modeling, numerical methods, optimization, statistics, probability, differential equations, and more. These tools are used to address practical problems across various domains, such as physics, engineering, finance, biology, and social sciences.

1. APPLICATION:

• Core Mathematics: While core mathematics may have applications in other fields, its primary focus is on developing mathematical theory and understanding mathematical structures for their own sake, rather than for immediate practical applications.
• Applied Mathematics: Applied Maths is directly concerned with solving real-world problems by employing mathematical methods and models. It seeks to provide solutions, insights, and predictions that can be applied in specific domains to address practical challenges and improve decision-making.

 Here we provide the solutions for CBSE Applied Maths problems for class 11 and 12 which is of specifics textbook “ML Aggarwal”. Applied Maths covers topics such as, calculus, differential equations, linear algebra, probability, statistics, and mathematical modeling, among others.

Here’s a general overview of some common topics covered in applied mathematics classes at the high school level:

• CALCULUS: Solutions involve differentiation, integration, limits, optimization, and applications of derivatives and integrals. Example problems might include finding derivatives or integrals of functions, solving optimization problems, and analyzing motion or growth using calculus.
• DIFFERENTIAL EQUATIONS: Solutions involve solving ordinary differential equations (ODEs) and understanding concepts such as first-order, second-order, linear, and nonlinear differential equations. Example problems might include solving initial value problems, modeling exponential growth or decay, or analyzing systems of differential equations.
• LINEAR ALGEBRA: Solutions involve understanding matrices, vectors, systems of linear equations, matrix operations, determinants, eigenvalues, and eigenvectors. Example problems might include solving systems of linear equations, finding inverses of matrices, or diagonalizing matrices.
• PROBABILITY ANS STATISTICS: Solutions involve understanding probability distributions, statistical measures, hypothesis testing, regression analysis, and probability calculations. Example problems might include finding probabilities, calculating expected values, conducting hypothesis tests, or fitting a regression model to data.
• MATHEMATICAL MODELLING: Solutions involve using mathematical tools to model real-world phenomena and solve practical problems. Example problems might include modeling population growth, analyzing rates of change in physical systems, optimizing production processes, or predicting financial trends.

Applied Maths Class 11 Chapters :

Applied Maths Class 12 Chapters :

Chapter – 1	Numbers, Quantifications and Numerical Applications
Chapter – 2	Numerical Inequalities
Chapter – 3	Matrices
Chapter – 4	Determinants
Chapter – 5	Differentiation
Chapter – 6	Applications of Derivatives
Chapter – 7	Integrals
Chapter – 8	Differential Equations
Chapter – 9	Probability
Chapter – 10	Inferential Statistics
Chapter – 11	Time – based Data
Chapter – 12	Perpetuity, Sinking Funds and EMI
Chapter – 13	Returns, Growth and Depreciation
Chapter – 14	Linear programming