Skip to main content Skip to page footer
TechMechAcademy logo TechMechAcademy logo

Mathematical Tools

Mechanical engineering deals with the analysis and description of mechanical systems, which are often complex and challenging to comprehend. To understand and analyze these systems, mathematical tools aids are indispensable.

Derivative rules, function equations, trigonometric functions, and other mathematical concepts are of great importance in mechanical engineering. With the help of these tools, complex motions and forces can be described and analyzed. The use of these concepts allows us to express mechanics in a language that enables us to apply mathematical methods to problem-solving.

Here you will find important mathematical tools that are essential for solving problems in mechanical engineering.

Content
  1. Derivative Rules
  2. Derivatives of Basic Functions
  3. Formulating Functional Equations
    1. Setting up Linear Functions
    2. Setting up Quadratic Functions (Parabolas)
  4. Table of Integrals
  5. Integration Rules
  6. Power Laws
  7. Triangle Similarity Theorems
  8. Trigonometry
    1. Angle Measures
      1. Conversion of Angle Measurements
    2. Definition of the Trigonometric Functions
      1. Trigonometric Functions on the Unit Circle
      2. Trigonometric Functions in a right-angled Triangle
      3. Quadrant Rule
    3. Sine and Cosine Functions
    4. The Tangent Function
    5. Important Relationships between the Trigonometric Functions
      1. Relationship between Sine and Cosine
      2. Trigonometric Pythagorean Theorem
      3. Elementary Relationships between Sine, Cosine, Tangent, and Cotangent Functions
      4. Conversions between Trigonometric Functions
    6. Formulas for Trigonometric Functions
      1. Addition Theorems for Calculating the Sum and Difference of Angle Values
      2. Formulas for Half-Angles
      3. Formulas for Double Angles
      4. Formulas for Triple Angles
      5. Formulas for Powers of Trigonometric Terms
      6. Formulas for Sums and Differences of Trigonometric Terms
      7. Formulas for Products of Trigonometric Terms
  9. Root Laws