1. Generalized Quantum Differentiation
1.1 The ß-Operator
1.2 Definition for ß-Derivative. Examples
1.3 Properties of the ß-Derivative
1.4 Rules for ß-Differentiation
1.5 Properties of ß-Differentiable Functions
1.6 Chain Rules
1.7 A Mean Value Theorem
1.8 Higher Order ß-Derivatives
1.9 Advanced Practical Problems
1.10 Notes and References

2. Generalized Quantum Integration
2.1 ß-Antiderivatives
2.2 Definition for ß-Integral. Examples
2.3 Properties of ß-Integrals
2.4 Inequalities and ß-Integrals
2.5 Generalized Quantum Monomials
2.6 The Taylor Formula
2.7 Improper Integrals of the First Kind
2.8 Improper Integrals of the Second Kind
2.9 Advanced Practical Problems
2.10 Notes and References

3. ß-Elementary Functions
3.1 ß- Regressive Functions
3.2 ß-Exponential Functions
3.3 ß-Trigonometric Functions
3.4 ß-Hyperbolic Functions
3.5 Advanced Practical Problems
3.6 Notes and References

4. The ß-Laplace Transform
4.1 Functions of Exponential Orders
4.2 Definition for the ß-Laplace Transform. Properties
4.3 The ß-Laplace Transform of ß-Derivative
4.4 The ß-Laplace Transform of ß-Integrals
4.5 Advanced Practical Problems
4.6 Notes and References

5. First Order Linear ß-Differential Equations
5.1 Linear ß-Differential operators
5.2 Homogeneous Initial Value Problems
5.3 Nonhomogeneous Initial Value Problems
5.4 The Laplace Transform Method
5.5 Notes and References

6. Second Order Linear ß-Differential Equations
6.1 ß-Wronskians
6.2 The Abel Theorem
6.3 Homogeneous Second Order Linear ß-Differential Equations with Constant Coefficients
6.4 Reduction of Order
6.5 Method of Factoring
6.6 Nonconstant Coefficients
6.7 ß-Euler-Cauchy Equations
6.8 Variation of Parameters
6.9 The Anihilator Method
6.10 The ß-Laplace Transform Method
6.11 Advanced Practical Problems
6.12 Notes and References

7. ß-Differential Systems
7.1 Structure of ß-Differential Systems
7.2 ß-Matrix Exponential Function
7.3 The ß-Liouville Theorem
7.4 Constant Coefficients
7.5 Advanced Practical Problems
7.6 Notes and References

8. Linear ß- Integral Inequalities
8.1 Gronwall-Type Inequalities
8.2 Bellman-Type Inequalities
8.3 Volterra-Type ß-Integral Inequalities
8.4 Notes and References