MATH1013 Mathematics And Applications 1 Notes | Assignment Help | Syllabus
University: Australian National University
“Single-variable calculus and basic linear algebra are covered in this course. The focus will be on comprehending the subject so that it may be used in a variety of disciplines, such as physical and biological sciences, engineering and computer technologies, economics and business, and as a foundation for subsequent mathematics courses. Many applications and links to other disciplines will be mentioned, but not further developed. The content will not be produced in a strict theorem-proof manner. MATH1115 is for students who want to learn more about mathematics or the mathematical/theoretical elements of subjects like engineering, physics, and economics.
The following are some of the topics that will be discussed:
Limits in calculus, include infinite and infinity limits. Continuous functions’ continuity and global characteristics. Differentiation, includes the mean value theorem, the chain rule, implicit differentiation, inverse functions, antiderivatives, and fundamental differential equations concepts. Exponential and logarithmic functions, as well as their connections to integration, growth and decay, and hyperbolic functions, are examples of transcendental functions. Concavity and inflection points, as well as local and absolute extrema. The reign of L’Hopital. The Fundamental Theorem of Calculus and Riemann Integration Integration techniques include the replacement approach and part-by-part integration. Volumes.
Linear Algebra is the study of how to solve linear systems of equations. Matrix inverses, partitioned matrices, linear transformations, matrix factorization, and subspaces are all covered in matrix algebra. Determinants. Graphics, the Leontief Input-Output Model, and other linear models in science and engineering are examples of uses. Numbers that are difficult to understand. The emphasis is on learning and using algorithms.
After successfully completing the course, students will be able to:
Explain the basic principles of calculus and linear algebra, as well as their applications in contemporary mathematics. Limits, continuity, differentiation, local and absolute extrema, Riemann integration, and the fundamental theorem of calculus are some of the concepts covered in Linear Algebra, as well as limits, continuity, differentiation, local and absolute extrema, Riemann integration, and the fundamental theorem of calculus in Calculus.
Demonstrate the correct and efficient use of calculus and linear algebra methods to the topics mentioned above.
Explaining ideas from calculus and linear algebra will demonstrate your ability to think mathematically.
Apply calculus and linear algebra problem-solving methods to a variety of problems in physics, engineering, and other mathematical settings.”
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