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The syllabus for an applied mathematics course can vary depending on the institution and the level of the course (undergraduate, postgraduate, etc.). However, I can provide you with a general overview of the topics commonly covered in an applied mathematics course. Here are some of the key areas typically included in the syllabus:

1. Calculus: Limits, differentiation, integration, differential equations, partial derivatives, multiple integral, vector calculus.

2. Linear Algebra: Vector space, matrices, determinants, systems of linear equations, eigenvalues and eigenvectors, linear transformation.

3. Probability and Statistics: Probability theory, random variables, probability distributions, statistical inference, hypothesis testing, regression analysis, stochastic processes.

4. Numerical Methods: Numerical approximation techniques, root finding methods, numerical integration, interpolation, solving differential equations numerically.

5. Differential Equations: Ordinary differential equations, partial differential equations, boundary value problems, applications in physics, engineering, and other fields.

6. Optimization: Optimization theory, contained and unconstrained optimization problems, linear programming, nonlinear programming.

7. Mathematical Modelling: Techniques for formulating mathematical model of real-world problems, analysis and interpretation of model results.

8. Complex Analysis: Complex numbers, functions, integration, series, resides, conformal mapping.

9. Discrete Mathematics: Combinatorics, graph theory, set theory, logic, algorithms, discrete optimization.

10. Mathematical Physics: Applications of mathematics in physics, including mathematical methods used in classical mechanics, quantum mechanics, electromagnetism, and fluid dynamics.

It's important to note that this is a general outline, and the specific syllabus may vary from one institution to another. I recommend referring to the syllabus provided by the institution offering the applied mathematics course or consulting the course coordinator for the most accurate and detailed information.

Additional, textbooks and reference materials recommended by the institution can provide further insights into the specific topics and subtopics covered in the course.