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Abstract:In this paper, modern numerical continuation methodologies are presented as a way of understanding and computing multiplicity of solutions in undergraduate physics problems. Mechanical and thermodynamical problems are used as a storyline to introduce the mathematical formalism required to make clear the distinction between uniqueness and multiplicity of equilibrium solutions and critical states of a nonlinear physical problem as well as to illustrate how these novel numerical continuation techniques are implemented in practice. The paper provides simple numerical Matlab codes easily adaptable to other problems as well as updated software and literature resources currently available. CONFIDENTIAL -FOR REVIEW ONLY EJP-100348.R4Numerical AbstractIn this paper, modern numerical continuation methodologies are presented as a way of understanding and computing multiplicity of solutions in undergraduate physics problems. Mechanical and thermodynamical problems are used as a storyline to introduce the mathematical formalism required to make clear the distinction between uniqueness and multiplicity of equilibrium solutions and critical states of a nonlinear physical problem as well as to illustrate how these novel numerical continuation techniques are implemented in practice. The paper provides simple numerical Matlab codes easily adaptable to other problems as well as updated software and literature resources currently available.