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Advanced Mathematics – Year 12

Advanced Mathematics – Year 12

By admin Categories: Maths
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About Course

Course Overview: Deepen your understanding of advanced mathematical concepts and applications. This course covers topics in calculus, algebra, statistics, and more, preparing you for higher education and real-world challenges.

What Will You Learn?

  • This Year 12 Mathematics course delves into advanced mathematical concepts and applications, preparing students for higher-level studies and professional pursuits. Through engaging lessons and challenging assignments, students will develop critical thinking skills and a deep appreciation for the beauty and applicability of mathematics.

Course Content

Lesson 1: Course Introduction and Objectives
o Welcome to the course and understand its structure.

Lesson 2: Techniques of Integration
o Explore integration by parts, trigonometric substitution, and partial fractions. o Apply integration techniques to solve complex integrals.

Lesson 3: Applications of Differential Equations
o Study first-order and second-order differential equations. o Analyze real-world applications, including growth and decay models.

Lesson 4: Matrices and Systems of Equations
o Introduce matrices, matrix operations, and systems of linear equations. o Solve systems of equations using matrix methods.

Lesson 5: Matrix Transformations and Eigenvalues
o Explore linear transformations and matrix representations. o Study eigenvalues, eigenvectors, and diagonalization.

Lesson 6: Hyperbolic Functions and Their Properties
o Introduce hyperbolic functions and their properties. o Explore hyperbolic identities and applications.

Lesson 7: Complex Analysis and Residue Theorem
o Study complex numbers, complex functions, and contour integration. o Apply the residue theorem to calculate complex integrals.

Lesson 8: Set Theory and Logic
o Explore set theory, set operations, and Venn diagrams. o Understand propositional and predicate logic.

Lesson 9: Proof Techniques and Mathematical Induction
o Develop skills in proof writing and logic. o Study mathematical induction and its applications.

Lesson 10: Probability Distributions and Sampling
o Study continuous and discrete probability distributions. o Explore sampling methods and Central Limit Theorem.

Lesson 11: Hypothesis Testing and Confidence Intervals
o Understand hypothesis testing, p-values, and significance. o Calculate confidence intervals and perform statistical tests.

Lesson 12: Multivariable Calculus and Partial Derivatives
o Explore functions of several variables and partial derivatives. o Analyze critical points and optimize multivariable functions.

Lesson 13: Applications of Calculus to Physics and Engineering
o Apply calculus concepts to physics and engineering problems. o Study applications in kinematics, work, and fluid dynamics.

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